p-nilpotence of finite groups and minimal subgroups

[摘要] In this paper, it is proved that a finite group G is p-nilpotent if every minimal subgroup of P boolean AND O-p(G) is permutable in P and N-G(P) is p-nilpotent, and when p = 2 either [Omega(2) (P boolean AND O-p(G)), P] less than or equal to Omega(1)(P boolean AND O-p(G)) or P is quaternion-free, where p is a prime dividing the order of G and P is a Sylow p-subgroup of G. By using this result, we may get a series of corollaries for p-nilpotence, which contain some known results. Some other applications of this result are also given. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-12-15