共轭置换子群对群p-幂零性的影响

Influences of Self-conjugate Permutable Subgroups on p-nilpotence of Finite Groups

群G的一个子群H称为自共轭置换子群,如果对于g∈G,由HHg=HgH可推出H=Hg.本文利用p阶及4阶循环子群的自共轭置换性讨论有限群的结构,给出了此类群的结构描述.

A subgroup H of a group G is called self-conjugate permutable, if HH = H H implies that H= H for any g G. In this paper, the author studies the structure of finite groups by means of the self-conjugate permutability of cyclic groups of order and 4, some results for the structure are obtained.