弱s-条件置换子群与有限群的p-超可解性

Weakly s-Conditionally Permutable Subgroups and p-Supersolvability of Finite Groups

称群G的一个子群H在G中弱s-条件置换的,如果存在G的一个正规子群B使得G=HB,且对B的任意Sylow子群T,存在b∈B使得HTb=Tb H.笔者利用弱s-条件置换子群研究有限群的p-超可解性,推广了相关文献的一些结果.

A subgroup B of a finite group G is called weakly s-conditionally permutable subgroup of G if there exists a normal subgroup B of G such that G= FIB and for every Sylow subgroup T of B , there exists an element b ∈ B such that HTb = TbH . The influence of weakly s -conditionally permutable subgroup on p -su- persolvability of finite groups. The results obtained generalized some known works in the literatures.