有限群的π-拟正规嵌入子群

设G是有限群,称G的子群H在G中π-拟正规嵌入,如果对于|H|的每个素因子p,H的Sylowp-子群也是G的某个π-拟正规子群的Sylow p-子群.利用子群的π-拟正规嵌入性,得到了有限群G为p-幂零群的一些充分条件:设G是有限群,P是G的一个Sylow p-子群,其中p是|G|的一个素因子且使得(|G|,p-1)=1.若P的所有极大子群皆在NG(P)中π-拟正规嵌入且NG(P)’也在G中π-拟正规嵌入,则G为p-幂零群.推广并加深了一些已知结果.

On π-quasinormal Embedded Subgroups of Finite Groups

Let G be a finite group.A subgroup H of G is said to be π-quasinormally embeddable in G,if for each prime divisor p of the order of H,a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroup of G.In terms of the properties of π-quasinormally embeddability,some sufficient conditions for p-nilpotent of finite groups are obtained.Let G be a finite group and p a prime divisor of |G| with(|G|,p-1)=1.If there exists a Sylow p-subgroup P of G such that every maximal subgroup of P is π-quasinormal embeddable in NG(P) and NG(P)′ is π-quasinormally embeddable in G,then,G is p-nilpotent.And some known results are generalized and improved.