自共轭置换子群对群p-幂零性的影响

The Influence of Self-conjugate Permutable Subgroups on p-nilpotency of Finite Groups

有限群G的一个子群H叫做自共轭置换子群,如果对于任意x∈G,由HHx=HxH可推出H=Hx.通过研究p阶和4阶循环子群的自共轭置换性来讨论有限群的p-幂零性.

A subgroup H of a finite group G is called a self-conjugate permutable subgroup in G,if HHx=HxH implies that H=Hx for any x of G.In this paper,the p-nipotency of finite groups by means of the self-conjugate permutability of cyclicgroups of order p and 4 are studied.