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
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
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 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 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
A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups...A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.展开更多
In this paper,finite p-groups G with G/HGbeing cyclic for every minimal nonnormal subgroup H are classified up to isomorphism,where HGdenotes the normal closure of H.
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
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 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 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.
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.
文摘A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1137123211226048+1 种基金11401355)the Natural Science Foundation of Shanxi Province(Grant No.2013011001-1)
文摘In this paper,finite p-groups G with G/HGbeing cyclic for every minimal nonnormal subgroup H are classified up to isomorphism,where HGdenotes the normal closure of H.
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.
