p－拟正规与p－幂零

p-QUASI-NORMAL AND p-NILPOTENT

本文讨论了下述问题：当有限群Ｇ的一个Ｓｙｌｏｗｐ－子群的所有极大（２－极大）子群都是Ｇ的ｐ－拟正规子群时，Ｇ为ｐ－幂零群的条件。

in this paper, we prove the following conclusion:Suppose that P∈Syl_p(G),and p∈π(G),then G is a p-nilpotent group, if G satisfies one of the four following conditions:(1) every maximal subgroup of P is p-quasi-normal in G,and Hc(P)/CG(P) is a p-group;(2) p is the minimum element in π(G),every maximal subgroup of P is p-quasi-normal in G,and G is irrelevant with the minimal non-nilpotent p-basic groups of order p￣aq;(3) every 2-maximal subgroup of P is p-quasi-normal in G,NG(P)/Cc(P) is a p-group,and G is irrelevant with the p-basic groups of order p￣2q;(4) p is the minimum element is π(G),every 2-maximal subgroup of P is p-quasi-normal in G,and G is irrelevant with the minimal non-nilpotent p-basic groups of order p￣aq.