Let G be a finite group.Let D={(g,g)|g∈C},the main diagonalsubgroup of G x G.In this paper,we consider the suitable generalized normalities orindex of D in G x G,some interesting results are obtained.
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
基金the NSF of China(Nos.11201082,11471054,11671063),the NSF of Jiangsu Province(No.BK20161265)Cultivation Program for Outstanding Young College Teachersof Guangdong Province(Yq2013061).
文摘Let G be a finite group.Let D={(g,g)|g∈C},the main diagonalsubgroup of G x G.In this paper,we consider the suitable generalized normalities orindex of D in G x G,some interesting 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.
