SS-拟正规子群对有限群p-超可解性的影响

Influence of SS-quasinormal subgroups on the p-supersolvability of finite groups

设G为有限群,若存在B≤G使得G=HB,且对任意p∈π(B),P∈Sy1_( p)(B),都有HP=PH,则称子群H在G中SS-拟正规.利用极小阶反例法,讨论某些p-子群SS-拟正规的有限群结构,得到p-超可解群的若干充分条件,推广了p-超可解性的部分结果.

Let G be a finite group.A subgroup H is said to be SS-quasinormal in G if there is a subgroup B of G such that G=HB,and H permutes with any Sylow p-subgroup of B for arbitrary prime p∈π(B).The structures of finite groups with SS-quasinormality of some p-subgroups are discussed by using counterexample of minimal order,and several sufficient conditions of p-supersolvable groups are obtained,which generalize some known results of p-supersolvability.