弱c#-正规子群与有限群的p-幂零性

Weakly c#-Normal Subgroups and the p-nilpotency of Finite Groups

利用弱c#-正规子群研究有限群的p-幂零性,得到以下结论:①设G是群,HG,使得G/H为p-幂零,P∈Sylp(G),若P的极大子群皆在G中弱c#-正规且NG(P)为p-幂零,则G为p-幂零.②G是群,HG使得G/H为p-幂零,P∈Sylp(H),若P的2-极大子群皆在G中弱c#-正规且NG(P)为p-幂零的,则G为p-幂零.

The influence of Weakly c#-normal Subgroup on the p-nilpotency of finite groups is investigated. （1）Let G be a finite group, H△G, and G/H is p-nilpotent, Pff sy/p（G）, if every maximal subgroup of P is a weakly c#-normal subgroup of G, and Nc.（P） is p-nilpotent, then G is p-nilpotent. （2） Let G be a finite group, H△G and G/H is p-nilpotent, P∈ sylp（H）, if every second maximal subgroup of P is a weakly c#-normal subgroup of G and NG（P） is p- nilpotent, then G is p-nilpotent.