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.
Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing │H│, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal sub...Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing │H│, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called c^＊-quasinormally embedded in G if there is a subgroup T of G such that G = HT and HCqT is s-quasinormally embedded in G. We investigate the influence of c^＊-quasinormally embedded subgroups on the structure of finite groups. Some recent results are generalized.展开更多
Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md（P...Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md（P） = {P1,...,Pd}, such that di=1 Pi = Φ（P）, the Frattini subgroup of P. In this paper, we will show that if each member of some fixed Md（P） is either p-cover-avoid or S-quasinormally embedded in G, then G is p-nilpotent. As applications, some further results are obtained.展开更多
Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably embedded in G if for each prime p dividing ｜H｜, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgrou...Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably embedded in G if for each prime p dividing ｜H｜, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgroup of G; H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G = HT and H n T ≤ Hse. In this paper, we continue the work of [Comm. Algebra, 2009, 37： 1086-1097] to study the influence of the weakly s-permutably embedded subgroups on the structure of finite groups, and we extend some recent results.展开更多
Let G be a finite group,σ={σi|i∈ I}be some partition of the set of all primes and σ(G)={(σi|σi∩ π(G)≠0}.We say that a subgroup H of G is nearly cr-cmbcdded in G if there exists a cr-permutable subgroup T of G...Let G be a finite group,σ={σi|i∈ I}be some partition of the set of all primes and σ(G)={(σi|σi∩ π(G)≠0}.We say that a subgroup H of G is nearly cr-cmbcdded in G if there exists a cr-permutable subgroup T of G such that H∩T is a<r-permutable subgroup of G and H C\T<HaeG^where Haec is the subgroup of H generated by all those subgroups of H which are cr-permutably embedded in G.In this paper,we study the structure of G under the condition that some given subgroups of G are nearly cr-embedded in G.Some known results are generalized.展开更多
Let G be a finite group,and H a subgroup of G.H is called s-permutably embedded in G if each Sylow subgroup of H is a Sylow subgroup of some s-permutable subgroup of G.In this paper,we use s-permutably embedding prope...Let G be a finite group,and H a subgroup of G.H is called s-permutably embedded in G if each Sylow subgroup of H is a Sylow subgroup of some s-permutable subgroup of G.In this paper,we use s-permutably embedding property of subgroups to characterize the p-supersolvability of finite groups,and obtain some interesting results which improve some recent results.展开更多
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This work was supported in part by the National Natural Science Foundation of China （Grant No. 11071229） and the Natural Science Foundation the Jiangsu Higher Education Institutions （Grant No. J0KJD110004）.
文摘Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing │H│, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called c^＊-quasinormally embedded in G if there is a subgroup T of G such that G = HT and HCqT is s-quasinormally embedded in G. We investigate the influence of c^＊-quasinormally embedded subgroups on the structure of finite groups. Some recent results are generalized.
基金Supported by the National Natural Science Foundation of China (Grant No.10571181)the National Natural Science Foundation of Guangdong Province (Grant No.06023728) the Specialized Research Fund of Guangxi University (Grant No.DD051024)
文摘Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md（P） = {P1,...,Pd}, such that di=1 Pi = Φ（P）, the Frattini subgroup of P. In this paper, we will show that if each member of some fixed Md（P） is either p-cover-avoid or S-quasinormally embedded in G, then G is p-nilpotent. As applications, some further results are obtained.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271085, 11201082）, the Natural Science Foundation of Guangdong Province （S2011010004447）, and the Special Project for the Subject Build of High Education of Guangdong Province （2012KJCX0081）.
文摘Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably embedded in G if for each prime p dividing ｜H｜, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgroup of G; H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G = HT and H n T ≤ Hse. In this paper, we continue the work of [Comm. Algebra, 2009, 37： 1086-1097] to study the influence of the weakly s-permutably embedded subgroups on the structure of finite groups, and we extend some recent results.
文摘Let G be a finite group,σ={σi|i∈ I}be some partition of the set of all primes and σ(G)={(σi|σi∩ π(G)≠0}.We say that a subgroup H of G is nearly cr-cmbcdded in G if there exists a cr-permutable subgroup T of G such that H∩T is a<r-permutable subgroup of G and H C\T<HaeG^where Haec is the subgroup of H generated by all those subgroups of H which are cr-permutably embedded in G.In this paper,we study the structure of G under the condition that some given subgroups of G are nearly cr-embedded in G.Some known results are generalized.
基金supported by National Natural Science Foundation of China (Grant Nos. 11201082 and 11171353)China Postdoctoral Science Foundation (Grant Nos. 2012M521724 and 2013T60866)Natural Science Foundation of Guangdong Province (Grant No. S201204007267)
文摘Let G be a finite group,and H a subgroup of G.H is called s-permutably embedded in G if each Sylow subgroup of H is a Sylow subgroup of some s-permutable subgroup of G.In this paper,we use s-permutably embedding property of subgroups to characterize the p-supersolvability of finite groups,and obtain some interesting results which improve some recent results.
