有限群的可补置换子群与p-幂零性

SS-quasinormality of Subgroups and the p-nilpotency of Finite Groups

有限群G的子群H称为G的SS-拟正规子群,如果存在G的子群B,使得G=HB且对B的每个Sylow子群Q,都有HQ=QH.利用幂指数等于Sylowp-子群幂指数的交换p-子群的SS-拟正规性,来研究有限群的p-幂零性,推广和改进了一些已有的结果.

A subgroup H of a finite group G is said to be SS-quasinormal in G if there exists a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, some conditions for a finite group to be p-nilpotent are given using SS-quasinormality of some abelian subgroups with prime power order, and several known results are generalized and improved.