Let G be a group and H;K be subgroups of G.H is called a TI-subgroup of G if H∩H^(g)=1 or H for every g∈G.K is called P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G suc...Let G be a group and H;K be subgroups of G.H is called a TI-subgroup of G if H∩H^(g)=1 or H for every g∈G.K is called P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G such that|K_(i):K_(i-1)|∈P for i∈{1;2;…;n}.Furthermore,K is called K-P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G such that either K_(i-1)is normal in Ki or|K_(i):K_(i-1)|∈P for i∈{1;2;…;n}.In this paper,some properties of a nite group in which some particular subgroups are TI-subgroups or P-subnormal subgroups or K-P-subnormal subgroups are given.展开更多
Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤K■G.Let p be a prime which divide...Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤K■G.Let p be a prime which divides the order of a group G.In this paper,some characterizations of G being p-solvable or p-supersolvable were obtained by analyzing the normal index of certain subgroups of G.These results can be viewed as local version of recent results in the literature.展开更多
This paper investigates the in uence of local SS-quasinormal maximal subgroups of Sylow subgroups on the structure of nite groups.We present several new criteria on p-nilpotency of nite groups by utilizing a small qua...This paper investigates the in uence of local SS-quasinormal maximal subgroups of Sylow subgroups on the structure of nite groups.We present several new criteria on p-nilpotency of nite groups by utilizing a small quantity of local SS-quasinormal maximal subgroups of Sylow p-subgroups.As applications,we obtain some sucient conditions for a nite group to be in a saturated formation containing the class of supersolvable groups.展开更多
Let G be a finite group.A subgroup H of G is said to be σ-c-propermutable in G if G has a subgroup B such that G=N_(G)(H)B and for every Hall σ_(i)-subgroup B_(i) of B,there exists an element x∈B such that HB_(i)^(...Let G be a finite group.A subgroup H of G is said to be σ-c-propermutable in G if G has a subgroup B such that G=N_(G)(H)B and for every Hall σ_(i)-subgroup B_(i) of B,there exists an element x∈B such that HB_(i)^(x)=B_(i)^(x) H.In this paper,the influence of σ-c-propermutable subgroups on the structure of finite groups is investigated,and some criteria for a normal subgroup of G to be hypercyclically embedded in G are derived.展开更多
In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the r...In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the relationship between the core and the second maximal subgroups in these classifications.展开更多
Autonomous vehicles operate without direct human intervention,which introduces safety risks that differ from those of conventional vehicles.Although many studies have examined safety issues related to autonomous drivi...Autonomous vehicles operate without direct human intervention,which introduces safety risks that differ from those of conventional vehicles.Although many studies have examined safety issues related to autonomous driving,high-risk situations have often been defined using single indicators,making it difficult to capture the complex and evolving nature of accident risk.To address this limitation,this study proposes a structured framework for defining and analyzing high-risk situations throughout the traffic accident process.High-risk situations are described using three complementary indicators:accident likelihood,accident severity,and accident duration.These indicators explain how risk emerges,increases,and persists over time.Based on this concept,a framework for traffic accident visualization analysis is developed to support phase-specific risk assessment and visualization.The framework combines accident-phase information with factor-level risk contributions,allowing systematic identification of key factors and their interactions across different accident stages.Using combinations of the three indicators,high-risk situations are classified into twenty-seven distinct types,providing a clear typology for complex accident scenarios involving autonomous vehicles.The applicability of the proposed framework is demonstrated through two representative accident scenarioswith different risk characteristics.The results showthat the framework effectively captures interactions among multiple risk factors,explains how risk levels change from pre-crash to post-crash phases,and identifies contributing factors that are difficult to detect using conventional traffic accident investigation methods.Overall,the proposed framework offers a practical basis for autonomous vehicle accident analysis,safety evaluation,and policy-related decision-making.展开更多
Objective:To analyze the impact of maternal-infant separation on the physical and mental state of high-risk pregnancy patients and explore the clinical efficacy of targeted nursing interventions.Methods:A total of 80 ...Objective:To analyze the impact of maternal-infant separation on the physical and mental state of high-risk pregnancy patients and explore the clinical efficacy of targeted nursing interventions.Methods:A total of 80 high-risk pregnancy patients treated in our hospital from January 2023 to January 2024 were selected as the study subjects.These patients were randomly divided into an observation group and a control group(40 cases each)using a random number table.The control group received routine high-risk pregnancy nursing care,while the observation group received specialized maternal-infant separation nursing interventions in addition to routine care.The psychological and physiological states and nursing satisfaction of the two groups were compared before and after the intervention.Results:The SAS scores,SDS scores,and sleep quality scores of the observation group were significantly lower than those of the control group,with statistically significant differences(p<0.05).The incidence of postpartum hemorrhage in the observation group was significantly lower than that in the control group,and the initiation time of lactation was significantly earlier than that in the control group,with both differences being statistically significant(p<0.05).The nursing satisfaction of the observation group was significantly higher than that of the control group(80%vs.32/40),with a statistically significant difference(p<0.05).Conclusion:Maternal-infant separation exacerbates anxiety and depression in high-risk pregnancy patients,reduces sleep quality,increases the risk of postpartum hemorrhage,and delays the initiation of lactation.Specialized nursing interventions for maternal-infant separation can improve the physical and mental state of high-risk pregnancy patients,reduce the incidence of postpartum complications,and enhance nursing satisfaction,making them worthy of clinical application and promotion.展开更多
Objective The aim of this study was to analyze the correlation between the levels of 12 cytokines in the cervical microenvironment and cervical intraepithelial neoplasia in patients with high-risk human papillomavirus...Objective The aim of this study was to analyze the correlation between the levels of 12 cytokines in the cervical microenvironment and cervical intraepithelial neoplasia in patients with high-risk human papillomavirus(HR-HPV)infection.Methods Female patients(n=73)with HR-HPV infection were enrolled and divided into a high-grade squamous intraepithelial lesion(HSIL)group(n=33)and a non-HSIL(N-HSIL)group(n=40),which include low-grade squamous intraepithelial lesions and inflammation.Healthy screening subjects(n=31)with negative HR-HPV results were enrolled as a control group.We examined contemporaneous plasma and secretory cytokines from 25 study subjects to investigate the difference between systemic cytokine profiles and the local microenvironment immunity using the Wilcoxon matched-pairs signed rank test.The 12 cytokines from cervical secretions were compared between the three groups using the Mann-Whitney test,and logistic regression was used to analyze HSIL and N-HSIL.Results There were statistical differences in eight cytokines(IL-2,IL-6,TNF-α,IFN-γ,IL-1β,IL-12p70,IFN-α,and IL-8)between cervical secretion and plasma of the same patient,and seven cytokines were statistically different between the control and other two groups.We selected four independent variables(TNF-α,IFN-γ,IL-12p70,and IFN-α)commonly identified by univariate regression analysis and non-parametric tests for multivariate logistic regression analysis.Based on this model,HSIL could be predicted in patients with HR-HPV infection,with the area under the curve being 0.76.Conclusion The systemic cytokine profile cannot reflect the local microenvironment immunity,and the occurrence of HSIL is related to the cytokine levels in the cervical microenvironment.展开更多
Prenatal exposure to bisphenols and metals has raised significant concerns regarding their potential impact on fetal development,particularly the risk of fetal chromosome numerical abnormalities(CNA).In this case-cont...Prenatal exposure to bisphenols and metals has raised significant concerns regarding their potential impact on fetal development,particularly the risk of fetal chromosome numerical abnormalities(CNA).In this case-control study,we analyzed bisphenol and metal concentrations in amniotic fluid of high-risk pregnant women undergoing amniocentesis.Concentrations of bisphenols and metals were measured using ultra-performance liquid chromatography-tandem mass spectrometry and inductively coupled plasma-mass spectrometry,respectively.Logistic regression and quantile-based g-computation were applied to evaluate individual and combined effects,while dose-response relationships were assessed using restricted cubic splines.Our findings indicated that bisphenol S(BPS),bisphenol Z(BPZ),bisphenol AF(BPAF),antimony(Sb),and vanadium(V)were significantly associated with an increased risk of CNA when analyzed individually,whereas manganese,iron,copper(Cu),nickel(Ni),and zinc(Zn)were significantly and inversely associated with CNA risk.Combined exposure to bisphenol and metal mixtures was associated with an increased risk of CNA in multi-pollutant models.Cu and Ni exhibited a positive additive interaction.Furthermore,BPS,BPZ,and BPAF were individually associated with an increased risk of Down syndrome,while Zn was associated with a decreased risk of Down syndrome.BPS,Sb,V,and Zn were individually associated with an increased risk of Klinefelter syndrome.These findings underscore the potential role of prenatal bisphenol and metal exposure in the pathogenesis of fetal CNA,highlighting both additive and synergistic effects.展开更多
A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-suppl...A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.展开更多
Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = ...Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.展开更多
The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second comm...The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.展开更多
In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
In the literature, p-nilpotency of the normalizers of p-subgroups has an important influence on finite p-nilpotent groups. In this paper, we extend the p-nilpotency to psupersolvability and choose every normal p-subgr...In the literature, p-nilpotency of the normalizers of p-subgroups has an important influence on finite p-nilpotent groups. In this paper, we extend the p-nilpotency to psupersolvability and choose every normal p-subgroups H of P such that |H| = pdand explore p-supersolvability of G by the conditions of weakly M-supplemented properties of H and psupersolvability of the normalizer NG(H), where 1 ≤ pd<|P |. Also, we study the p-nilpotency of G under the assumptions that NG(P) is p-nilpotent and the weakly M-supplemented condition on a subgroup K such that K_(p)■K and P′≤ K_(p) ≤ Φ(P), Kp is a Sylow p-subgroup K. To some extent, our main results can be regarded as generalizations of the Frobenius theorem.展开更多
Let τ be a subgroup functor and H a p-subgroup of a finite group G. Let G= G/H_G and H= H/H_G. We say that H is Φ-τ-supplement in G if G has a subnormal subgroup T and a τ-subgroup S contained in H such that G=H T...Let τ be a subgroup functor and H a p-subgroup of a finite group G. Let G= G/H_G and H= H/H_G. We say that H is Φ-τ-supplement in G if G has a subnormal subgroup T and a τ-subgroup S contained in H such that G=H T and H∩T≤SΦ（H）. In this paper,some new characterizations of hypercyclically embedability and p-nilpotency of a finite group are obtained based on the assumption that some primary subgroups are Φ-τ-supplement in G.展开更多
In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive se...In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive security) under three static(i.e. non q-based) assumptions. It is worth noting that only recently Waters gives a short ciphertext broadcast encryption system that is even adaptively secure under the simple assumptions. One feature of our methodology is that it is relatively simple to leverage our techniques to get adaptive security.展开更多
Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subg...Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.展开更多
文摘Let G be a group and H;K be subgroups of G.H is called a TI-subgroup of G if H∩H^(g)=1 or H for every g∈G.K is called P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G such that|K_(i):K_(i-1)|∈P for i∈{1;2;…;n}.Furthermore,K is called K-P-subnormal in G if there is a chain of subgroups K=K_(0)≤K_(1)≤K_(2)≤…≤K_(n-1)≤K_(n)=G such that either K_(i-1)is normal in Ki or|K_(i):K_(i-1)|∈P for i∈{1;2;…;n}.In this paper,some properties of a nite group in which some particular subgroups are TI-subgroups or P-subnormal subgroups or K-P-subnormal subgroups are given.
基金Supported by the National Natural Science Foundation of China(Grant No.12071092)Guangdong Basic and Applied Basic Research Foundation(Grant No.2025A1515012072)+1 种基金the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH051298)the Scientific Research Foundation of Bozhou University(Grant No.BYKQ202419).
文摘Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤K■G.Let p be a prime which divides the order of a group G.In this paper,some characterizations of G being p-solvable or p-supersolvable were obtained by analyzing the normal index of certain subgroups of G.These results can be viewed as local version of recent results in the literature.
基金Supported by NSF of China(12061011)NSF of Guangxi(2023GXN-SFAA026333)。
文摘This paper investigates the in uence of local SS-quasinormal maximal subgroups of Sylow subgroups on the structure of nite groups.We present several new criteria on p-nilpotency of nite groups by utilizing a small quantity of local SS-quasinormal maximal subgroups of Sylow p-subgroups.As applications,we obtain some sucient conditions for a nite group to be in a saturated formation containing the class of supersolvable groups.
文摘Let G be a finite group.A subgroup H of G is said to be σ-c-propermutable in G if G has a subgroup B such that G=N_(G)(H)B and for every Hall σ_(i)-subgroup B_(i) of B,there exists an element x∈B such that HB_(i)^(x)=B_(i)^(x) H.In this paper,the influence of σ-c-propermutable subgroups on the structure of finite groups is investigated,and some criteria for a normal subgroup of G to be hypercyclically embedded in G are derived.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1237101812201236)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.B240201093/2013)the Natural Science Foundation of the Anhui Higher Education Institutions(Grant No.2022AH051907)。
文摘In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the relationship between the core and the second maximal subgroups in these classifications.
基金supported by the Korea Institute of Police Technology(No.:RS-2024-00405603).
文摘Autonomous vehicles operate without direct human intervention,which introduces safety risks that differ from those of conventional vehicles.Although many studies have examined safety issues related to autonomous driving,high-risk situations have often been defined using single indicators,making it difficult to capture the complex and evolving nature of accident risk.To address this limitation,this study proposes a structured framework for defining and analyzing high-risk situations throughout the traffic accident process.High-risk situations are described using three complementary indicators:accident likelihood,accident severity,and accident duration.These indicators explain how risk emerges,increases,and persists over time.Based on this concept,a framework for traffic accident visualization analysis is developed to support phase-specific risk assessment and visualization.The framework combines accident-phase information with factor-level risk contributions,allowing systematic identification of key factors and their interactions across different accident stages.Using combinations of the three indicators,high-risk situations are classified into twenty-seven distinct types,providing a clear typology for complex accident scenarios involving autonomous vehicles.The applicability of the proposed framework is demonstrated through two representative accident scenarioswith different risk characteristics.The results showthat the framework effectively captures interactions among multiple risk factors,explains how risk levels change from pre-crash to post-crash phases,and identifies contributing factors that are difficult to detect using conventional traffic accident investigation methods.Overall,the proposed framework offers a practical basis for autonomous vehicle accident analysis,safety evaluation,and policy-related decision-making.
文摘Objective:To analyze the impact of maternal-infant separation on the physical and mental state of high-risk pregnancy patients and explore the clinical efficacy of targeted nursing interventions.Methods:A total of 80 high-risk pregnancy patients treated in our hospital from January 2023 to January 2024 were selected as the study subjects.These patients were randomly divided into an observation group and a control group(40 cases each)using a random number table.The control group received routine high-risk pregnancy nursing care,while the observation group received specialized maternal-infant separation nursing interventions in addition to routine care.The psychological and physiological states and nursing satisfaction of the two groups were compared before and after the intervention.Results:The SAS scores,SDS scores,and sleep quality scores of the observation group were significantly lower than those of the control group,with statistically significant differences(p<0.05).The incidence of postpartum hemorrhage in the observation group was significantly lower than that in the control group,and the initiation time of lactation was significantly earlier than that in the control group,with both differences being statistically significant(p<0.05).The nursing satisfaction of the observation group was significantly higher than that of the control group(80%vs.32/40),with a statistically significant difference(p<0.05).Conclusion:Maternal-infant separation exacerbates anxiety and depression in high-risk pregnancy patients,reduces sleep quality,increases the risk of postpartum hemorrhage,and delays the initiation of lactation.Specialized nursing interventions for maternal-infant separation can improve the physical and mental state of high-risk pregnancy patients,reduce the incidence of postpartum complications,and enhance nursing satisfaction,making them worthy of clinical application and promotion.
基金supported by the National Key Research and Development Program of China(2023YFC2308800)the Natural Science Foundation of Shanghai(25ZR1402053)the Key Discipline of Public Health of the Shanghai Municipal Health Commission(Grant No.GWVI-11.1-07).
文摘Objective The aim of this study was to analyze the correlation between the levels of 12 cytokines in the cervical microenvironment and cervical intraepithelial neoplasia in patients with high-risk human papillomavirus(HR-HPV)infection.Methods Female patients(n=73)with HR-HPV infection were enrolled and divided into a high-grade squamous intraepithelial lesion(HSIL)group(n=33)and a non-HSIL(N-HSIL)group(n=40),which include low-grade squamous intraepithelial lesions and inflammation.Healthy screening subjects(n=31)with negative HR-HPV results were enrolled as a control group.We examined contemporaneous plasma and secretory cytokines from 25 study subjects to investigate the difference between systemic cytokine profiles and the local microenvironment immunity using the Wilcoxon matched-pairs signed rank test.The 12 cytokines from cervical secretions were compared between the three groups using the Mann-Whitney test,and logistic regression was used to analyze HSIL and N-HSIL.Results There were statistical differences in eight cytokines(IL-2,IL-6,TNF-α,IFN-γ,IL-1β,IL-12p70,IFN-α,and IL-8)between cervical secretion and plasma of the same patient,and seven cytokines were statistically different between the control and other two groups.We selected four independent variables(TNF-α,IFN-γ,IL-12p70,and IFN-α)commonly identified by univariate regression analysis and non-parametric tests for multivariate logistic regression analysis.Based on this model,HSIL could be predicted in patients with HR-HPV infection,with the area under the curve being 0.76.Conclusion The systemic cytokine profile cannot reflect the local microenvironment immunity,and the occurrence of HSIL is related to the cytokine levels in the cervical microenvironment.
基金supported by the Key Project of Natural Science Foundation of Tianjin(No.23JCZDJC00330)Tianjin Municipal Education Commission Scientific Research Program(No.2022ZD056).
文摘Prenatal exposure to bisphenols and metals has raised significant concerns regarding their potential impact on fetal development,particularly the risk of fetal chromosome numerical abnormalities(CNA).In this case-control study,we analyzed bisphenol and metal concentrations in amniotic fluid of high-risk pregnant women undergoing amniocentesis.Concentrations of bisphenols and metals were measured using ultra-performance liquid chromatography-tandem mass spectrometry and inductively coupled plasma-mass spectrometry,respectively.Logistic regression and quantile-based g-computation were applied to evaluate individual and combined effects,while dose-response relationships were assessed using restricted cubic splines.Our findings indicated that bisphenol S(BPS),bisphenol Z(BPZ),bisphenol AF(BPAF),antimony(Sb),and vanadium(V)were significantly associated with an increased risk of CNA when analyzed individually,whereas manganese,iron,copper(Cu),nickel(Ni),and zinc(Zn)were significantly and inversely associated with CNA risk.Combined exposure to bisphenol and metal mixtures was associated with an increased risk of CNA in multi-pollutant models.Cu and Ni exhibited a positive additive interaction.Furthermore,BPS,BPZ,and BPAF were individually associated with an increased risk of Down syndrome,while Zn was associated with a decreased risk of Down syndrome.BPS,Sb,V,and Zn were individually associated with an increased risk of Klinefelter syndrome.These findings underscore the potential role of prenatal bisphenol and metal exposure in the pathogenesis of fetal CNA,highlighting both additive and synergistic effects.
文摘A subgroup H of a group G is called F-z-supplemented in G if there exists a subgroup K of G, such that G = HK and H∩K≤ Z∞F（G）, where Z∞F（G） is the F-hypercenter of G. We obtain some results about the F-z-supplemented subgroups and use them to determine the structure of some groups.
基金supported by the Deanship of Scientific Research(DSR) at King Abdulaziz University(KAU) represented by the Unit of Research Groups through the grant number(MG/31/01) for the group entitled "Abstract Algebra and its Applications"
文摘Let G be a finite group. A subgroup H of G is called an H-subgroup in G if NG（H）∩ H^g ≤ H for all g C G. A subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H N K is an H-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that every subgroup of G of prime order or of order 4 is a weakly H-subgroup in G. Our results improve and generalize several recent results in the literature.
文摘The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.
基金Supported by SRFPYED(2017ZDX041)and SRFPYED(2016ZDX151)
文摘In this paper, the influence of s-semipermutable, c~#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.
基金Supported by the National Natural Science Foundation of China(Grant No.12001436)the Natural Science Foundation of Sichuan Province(Grant No.2022NSFSC1843)+3 种基金Chunhui Plan Cooperative Scientific Research Project of Ministry of Education of the People’s Republic of Chinathe Fundamental Research Funds of China West Normal University(Grant Nos.17E09118B032)。
文摘In the literature, p-nilpotency of the normalizers of p-subgroups has an important influence on finite p-nilpotent groups. In this paper, we extend the p-nilpotency to psupersolvability and choose every normal p-subgroups H of P such that |H| = pdand explore p-supersolvability of G by the conditions of weakly M-supplemented properties of H and psupersolvability of the normalizer NG(H), where 1 ≤ pd<|P |. Also, we study the p-nilpotency of G under the assumptions that NG(P) is p-nilpotent and the weakly M-supplemented condition on a subgroup K such that K_(p)■K and P′≤ K_(p) ≤ Φ(P), Kp is a Sylow p-subgroup K. To some extent, our main results can be regarded as generalizations of the Frobenius theorem.
基金Supported by the National Natural Science Foundation of China(Grant No.11371335)
文摘Let τ be a subgroup functor and H a p-subgroup of a finite group G. Let G= G/H_G and H= H/H_G. We say that H is Φ-τ-supplement in G if G has a subnormal subgroup T and a τ-subgroup S contained in H such that G=H T and H∩T≤SΦ（H）. In this paper,some new characterizations of hypercyclically embedability and p-nilpotency of a finite group are obtained based on the assumption that some primary subgroups are Φ-τ-supplement in G.
基金supported by the Nature Science Foundation of China under grant 60970119, 60803149the National Basic Research Program of China(973) under grant 2007CB311201
文摘In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive security) under three static(i.e. non q-based) assumptions. It is worth noting that only recently Waters gives a short ciphertext broadcast encryption system that is even adaptively secure under the simple assumptions. One feature of our methodology is that it is relatively simple to leverage our techniques to get adaptive security.
文摘Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.
