关于有限群的共轭置换子群

On the Conjugate-permutable Subgroups of Finite Groups

群G的子群H称为在G中共轭置换,若HgH=HHg对任意的g∈G成立.本文利用共轭置换子群的概念研究了群的幂零性和超可解性的问题,获得了一个群为幂零群或超可解群的几个等价条件和充分条件.

A subgroup H of a group G is called conjugate-permutable in G if it is permutable with every conjugate subgroups Hg of H for all g∈G.In this paper,the influences of conjugate permutability on nilpotency and supersolvability of finite groups are investigated.Some equivalent and sufficient conditions for a group to be nilpotent and supersolvable are obtained.