自共轭置换子群对群结构的影响

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

群G的一个子群H叫做自共轭置换子群,如果对于HHx=HxH可推出Hx=H.文中利用自共轭置换子群的性质获得了幂零性和超可解性新的充分必要条件,推广了一些超可解性和幂零性的结果.

A subgroup H of G is said to be self-conjugate-permutable of HH^z=H^zH implies H^z = H. We obtain new sufficient and necessary conditions for supersolvability and nilpotency and extend some well-known results on the supersolvability and the nilpotency.