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
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 clinical research,subgroup analysis can help identify patient groups that respond better or worse to specific treatments,improve therapeutic effect and safety,and is of great significance in precision medicine.This...In clinical research,subgroup analysis can help identify patient groups that respond better or worse to specific treatments,improve therapeutic effect and safety,and is of great significance in precision medicine.This article considers subgroup analysis methods for longitudinal data containing multiple covariates and biomarkers.We divide subgroups based on whether a linear combination of these biomarkers exceeds a predetermined threshold,and assess the heterogeneity of treatment effects across subgroups using the interaction between subgroups and exposure variables.Quantile regression is used to better characterize the global distribution of the response variable and sparsity penalties are imposed to achieve variable selection of covariates and biomarkers.The effectiveness of our proposed methodology for both variable selection and parameter estimation is verified through random simulations.Finally,we demonstrate the application of this method by analyzing data from the PA.3 trial,further illustrating the practicality of the method proposed in this paper.展开更多
A subgroup H of a group G is said to be self-conjugate-permutable if HHx=H xH implies H^(x)=H for any x of G.A finite group G is called an SC-group(P SC-group,respectively)if all cyclic subgroups of G of order 2 or or...A subgroup H of a group G is said to be self-conjugate-permutable if HHx=H xH implies H^(x)=H for any x of G.A finite group G is called an SC-group(P SC-group,respectively)if all cyclic subgroups of G of order 2 or order 4(prime order or order 4,respectively)are selfconjugate-permutable in G.In this paper,we first investigate the structure of finite non-solvable groups all of whose second maximal subgroups are SC-groups;then we mainly investigate the structure of finite groups in which all of maximal subgroups of even order are P SC-groups.In fact,we describe the structure of finite groups which are not P SC-groups but all of whose maximal subgroups of even order are P SC-groups.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.
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
Let F be a class of finite groups. A subgroup H of a finite group G is said to be Fs-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable in G and （H／cap T）HG/HG is contained in th...Let F be a class of finite groups. A subgroup H of a finite group G is said to be Fs-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable in G and （H／cap T）HG/HG is contained in the F-hypercenter ZF∞ （G/HG） of G/HG. In this paper, we use Fs-quasinormal subgroups to study the structure of finite groups. Some new results are obtained.展开更多
Let H be a subgroup of a finite group G and p a prime divisor dividing the order of G.We say H is cp-supplemented in G if there exists a supplement T to H in G containing HGsuch that H∩T/HGis a p’-group,where HGis t...Let H be a subgroup of a finite group G and p a prime divisor dividing the order of G.We say H is cp-supplemented in G if there exists a supplement T to H in G containing HGsuch that H∩T/HGis a p’-group,where HGis the core of H in G.A CSp-group is a group in which every p-subgroup is cp-supplemented.In this paper,we characterize the p-solvability and psupersolvability of groups G with some certain p-subgroups being cp-supplemented.Furthermore,we give some equivalent conditions of CSp-group in p-solvable universe.Finally,we give some criteria of CSp-groups for the direct product of two CSp-groups.Our results extend some recent conclusions.展开更多
Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we inve...Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we investigate the structure of a finite group by θ*-completions of F-abnormal subgroups.展开更多
In this paper, we investegate the intersection of a maximal intransitive subgroup with a maximal imprimitive subgroup. And, the structure of the second maximal intransitive subgroup of an alternating group is determined.
Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this pape...Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.展开更多
In this note the author studies such a finite group in which each subgroup is either Sseminormal or selfnormal and characterizes this kind of finite groups.Moreover,the main results in[1] and [2] can be obtained by t...In this note the author studies such a finite group in which each subgroup is either Sseminormal or selfnormal and characterizes this kind of finite groups.Moreover,the main results in[1] and [2] can be obtained by the conclusion in this note.展开更多
A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditional...A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.展开更多
For a maximal subgroup M of a finite group G,a&-subgroup C is any subgroup of G suchthat C M and Core,(M(C)is maximal among normal subgroups of G properly contained in C.This paper is devoted to discussing the sol...For a maximal subgroup M of a finite group G,a&-subgroup C is any subgroup of G suchthat C M and Core,(M(C)is maximal among normal subgroups of G properly contained in C.This paper is devoted to discussing the solvability of finite groups and some new conditions are estab-lished which insure a group to be solvable.展开更多
In this paper .an important property layer-preserving of LF group and an concept LF λ-subgroup generated by LF subset will be introduced. On the height of LF group theory ,we recognize the concept generated subgroup ...In this paper .an important property layer-preserving of LF group and an concept LF λ-subgroup generated by LF subset will be introduced. On the height of LF group theory ,we recognize the concept generated subgroup more clearly.展开更多
A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable group...A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable groups to a saturated formation containing the class of finite supersolvable groups.展开更多
In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems ab...In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.展开更多
An exogenous avian leukosis virus (ALV) strain SDAU09C1 was isolated in DF-1 cells from one of 240 imported 1-day-old white meat-type grand parent breeder chicks. Inoculation of SDAU09C1 in ALV-free chickens induced a...An exogenous avian leukosis virus (ALV) strain SDAU09C1 was isolated in DF-1 cells from one of 240 imported 1-day-old white meat-type grand parent breeder chicks. Inoculation of SDAU09C1 in ALV-free chickens induced antibody reactions specific to subgroup A or B. But gp85 amino acid sequence comparisons indicated that SDAU09C1 fell into subgroup A; it had homology of 88.8%-90.3% to 6 reference strains of subgroup A, much higher compared to other subgroups including subgroup B. This is the first report for ALV of subgroup A isolated from imported breeders.展开更多
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.
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 Natural Science Foundation of Fujian Province(2022J011177,2024J01903)the Key Project of Fujian Provincial Education Department(JZ230054)。
文摘In clinical research,subgroup analysis can help identify patient groups that respond better or worse to specific treatments,improve therapeutic effect and safety,and is of great significance in precision medicine.This article considers subgroup analysis methods for longitudinal data containing multiple covariates and biomarkers.We divide subgroups based on whether a linear combination of these biomarkers exceeds a predetermined threshold,and assess the heterogeneity of treatment effects across subgroups using the interaction between subgroups and exposure variables.Quantile regression is used to better characterize the global distribution of the response variable and sparsity penalties are imposed to achieve variable selection of covariates and biomarkers.The effectiveness of our proposed methodology for both variable selection and parameter estimation is verified through random simulations.Finally,we demonstrate the application of this method by analyzing data from the PA.3 trial,further illustrating the practicality of the method proposed in this paper.
基金Supported by the National Natural Science Foundation of China(Grant No.12061030)the Natural Science Foundation of Hainan Province(Grant No.122RC652).
文摘A subgroup H of a group G is said to be self-conjugate-permutable if HHx=H xH implies H^(x)=H for any x of G.A finite group G is called an SC-group(P SC-group,respectively)if all cyclic subgroups of G of order 2 or order 4(prime order or order 4,respectively)are selfconjugate-permutable in G.In this paper,we first investigate the structure of finite non-solvable groups all of whose second maximal subgroups are SC-groups;then we mainly investigate the structure of finite groups in which all of maximal subgroups of even order are P SC-groups.In fact,we describe the structure of finite groups which are not P SC-groups but all of whose maximal subgroups of even order are P SC-groups.
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 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 the National Natural Science Foundation of China(Grant No.11071147)Doctoral Program Foundation of Institutions of Higher Education of China(Grant No.20113402110036)
文摘Let F be a class of finite groups. A subgroup H of a finite group G is said to be Fs-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable in G and （H／cap T）HG/HG is contained in the F-hypercenter ZF∞ （G/HG） of G/HG. In this paper, we use Fs-quasinormal subgroups to study the structure of finite groups. Some new results are obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.12071092)the Science and Technology Program of Guangzhou Municipality(Grant No.201804010088).
文摘Let H be a subgroup of a finite group G and p a prime divisor dividing the order of G.We say H is cp-supplemented in G if there exists a supplement T to H in G containing HGsuch that H∩T/HGis a p’-group,where HGis the core of H in G.A CSp-group is a group in which every p-subgroup is cp-supplemented.In this paper,we characterize the p-solvability and psupersolvability of groups G with some certain p-subgroups being cp-supplemented.Furthermore,we give some equivalent conditions of CSp-group in p-solvable universe.Finally,we give some criteria of CSp-groups for the direct product of two CSp-groups.Our results extend some recent conclusions.
文摘Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HGbelongs to F; otherwise H is said to be F-abnormal in G. In this paper, we investigate the structure of a finite group by θ*-completions of F-abnormal subgroups.
文摘In this paper, we investegate the intersection of a maximal intransitive subgroup with a maximal imprimitive subgroup. And, the structure of the second maximal intransitive subgroup of an alternating group is determined.
基金Yibin University Pre-research Project,Research on the coupling and coordinated development ofmanufacturing and logistics industry under the background of intelligentmanufacturing,(2022YY001)Sichuan ProvincialDepartment of EducationWater Transport EconomicResearch Center,Research on the Development Path and Countermeasures of the Advanced Manufacturing Industry in the Sanjiang New District of Yibin under a“dual circulation”development pattern(SYJJ2020A06).
文摘Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.
文摘In this note the author studies such a finite group in which each subgroup is either Sseminormal or selfnormal and characterizes this kind of finite groups.Moreover,the main results in[1] and [2] can be obtained by the conclusion in this note.
基金The Scientific Research Foundation of Sichuan Provincial Education Department of China(No.08zb082)
文摘A subgroup H of G is called s-conditionally permutable in G if for every Sylow subgroup T of G, there exists an element x ∈ G such that HTK = T^KH. In this paper, we investigate further the influence of s-conditionally permutability of some 2-maximal subgroups of the Sylow subgroup of G, on the structure of finite groups. New criteria for a group G being p-nilpotent are obtained.
文摘For a maximal subgroup M of a finite group G,a&-subgroup C is any subgroup of G suchthat C M and Core,(M(C)is maximal among normal subgroups of G properly contained in C.This paper is devoted to discussing the solvability of finite groups and some new conditions are estab-lished which insure a group to be solvable.
文摘In this paper .an important property layer-preserving of LF group and an concept LF λ-subgroup generated by LF subset will be introduced. On the height of LF group theory ,we recognize the concept generated subgroup more clearly.
文摘A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable groups to a saturated formation containing the class of finite supersolvable groups.
文摘In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.
基金supported by a grant from Shandong province and a grant (200803019) from the Ministry of Agriculturesupported by a grant from Shandong province and a grant (20080019) from the Ministry of Agriculture
文摘An exogenous avian leukosis virus (ALV) strain SDAU09C1 was isolated in DF-1 cells from one of 240 imported 1-day-old white meat-type grand parent breeder chicks. Inoculation of SDAU09C1 in ALV-free chickens induced antibody reactions specific to subgroup A or B. But gp85 amino acid sequence comparisons indicated that SDAU09C1 fell into subgroup A; it had homology of 88.8%-90.3% to 6 reference strains of subgroup A, much higher compared to other subgroups including subgroup B. This is the first report for ALV of subgroup A isolated from imported breeders.
