极大超可解子群与有限群的超可解性

Maximal Supersolvable Subgroups and Supersolubility of Finite Groups

设G为有限群。本文考虑G的所有极大超可解子群的交,利用这个新子群及其性质,得出有限群G为超可解的若干新判据,推广了有关文献的一些结果。

Let G be a finite group.This paper introduces a new subgroup,which characterizes the intersection of all maximal supersolvable subgroups of G.By using this subgroup and its properties,some new results about the supersolvability of a group are obtained,which extend some recent results.