设H是有限群G的正规子群使得G/H为p-幂零群,其中是|G|的一个素因子且(|G|p,-1)=1.如果存在H的Sylow p-子群P,使得P每个极大子群皆在N中ts-置换,并且N'或P'在G中ts-置换,那么G是p-幂零群,这里N=NG(P).
Let H be normal subgroup of a finite group G such that G/H is p-nilpotent,where p is a prime divisor of |G| with(|G|,p-1)=1.If there exists a Sylow p-subgroup P of H such that every maximal subgroup of P is ts-permutable in N and either N′ or P′ is ts-permutable in G,then,G is p-nilpotent,where N=NG(P).