摘要
设G为有限群,奇素数p∈π(G),P∈SylpG。本文主要证明了G可解,如果下述条件之一满足:(1)G的指数与p互素的非正规子群为SST—群,且当N_G(p)<G时,N_G(p)为p—幂零群;(2)N_G(p)为幂零Hall子群,且G的包含N_G(p)的所有真子群为SST—群。
Let G be a finite group, an odd prime pen(G) and P a Sylow p-subgroup. In this paper we have proved that G is solvable if G satisfies one of the following conditions. (1) Every non-normal subgroup H of G is a SST-group if (G:H, p)=1, and Na(P) is a p-nilpotent group if Na(P)<G; (2) Every proper subgroup of G which-contains No(P) is a SST-group, and No(P) is a Hall nilpotent subgroup.
出处
《重庆师范学院学报（自然科学版）》
1991年第3期45-47,共3页
Journal of Chongqing Normal University(Natural Science Edition)
关键词
有限群
SST-群
P-幂零群
SST-group,p-nilpotent group, Thompson subgroup
