共轭置换子群对有限群结构的影响

The influence of conjugate-permutable subgroups on structure of finite groups

群G的子群H称为G的共轭置换子群,若HxH=HHx,对任意x∈G都成立.本文利用共轭置换子群的定义,在文[1]的基础上,又给出了共轭置换子群的若干性质及有限群成为可解的几个充分条件,进而推广了文[1]中的部分结果.

A subgroup H of a group G is called conjugate-permutable in G, if it is permutable with all conjugate subgroups of H. In this paper, utilizing definition of conjugate-permutable subgroups and article[ 1] ,we give some properties about conjugate-permutable subgroups and some sufficient conditions of the conjugate-permutable subgroups on the structure of finite groups, Furthermore some results of[1] are generalized.