SS-拟正规性对有限群p-超可解性的影响

Influence of SS-quasinormality on the p-supersolvability of Finite Groups

设G为有限群,子群H称作在G中SS-拟正规,若存在B≤G使G=HB,且对任意p∈π(B),P∈Sylp (B),皆有HP=PH。借助p-子群的SS-拟正规性,刻画有限群的结构。应用内p-幂零群与p-可解外p-超可解群的结构和极小阶反例法,得出若干p-幂零群、p-超可解群的判别准则。

Let G be a finite group.A subgroup H is called SS-quasinormal in G if there exists a subgroup B of G such as G=HB,and HP=PH for arbitrary prime p ofπ(B)and P∈Sylp(B).The structures of finite groups are discussed by means of the SS-quasinormality of p-subgroups.Several criteria for a finite group to be p-nilpotent or p-supersolvable will be obtained by using the structure of inner p-nilpotent group or p-solvable outer p-supersolvable group and counterexample of minimal order.