子群的拟正规性对有限群结构的影响(英文)

The influence of F_s-quasinormality of subgroups on the structure of finite groups

设G是一个有限群,F是一个群类.群G的子群H称为在G中是Fs拟正规的,如果存在G的正规子群T,使得HT在G中s置换且(H∩T)HG/HG≤ZF∞(G/HG).本文利用Fs拟正规的概念,得到了一些有限群的新刻画.

Let G be a finite group and F a class of groups.A subgroup H of 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∩T）HG/HG is contained in the F-hypercenter ZF∞（G/HG） of G/HG.In this paper,some new characterizations of finite groups are obtained by using the concept of Fs-quasinormal subgroups,and some known results are generalized.