中文摘要：

设G是有限群,称群G的子群H为G的NS-拟正规子群,如果对于满足（p,｜H｜）=1的每个素数p和适合H≤L≤G的每个子群L,均有NL（H）包含L的某个Sylowp-子群。称群G的子群H为G的NS^＊-拟正规子群,如果G有正规子群K使得G=HK,且H∩K为G的NS-拟正规子群。本文主要讨论p阶及p2阶子群的NS^＊-拟正规性对群G的p-幂零性的影响,得到群G为p-幂零的若干充分条件。

英文摘要：

Let Gbe a finite group.A subgroup H of Gis said to be an NS-quasinormal subgroup of Gif for every prime psuch that（p,｜H｜）=1and for every subgroup Lof Gcontaining H,the normalizer NL（H）contains some Sylow p-subgroup of L.A subgroup H of Gis said to be an NS^＊-quasinormal subgroup of Gif Ghas a normal subgroup Ksuch that G=HK,and H∩Kis an NS-subgroup of G.In this paper,by using NS^＊-quasinormal subgroups of order por p^2,some sufficient conditions for Gto be p-nilpotent are obtained.