On p-nilpotency and minimal subgroups of finite groups

作     者：郭秀云 K.P.Shum 

作者机构：Department of Mathematics Shanxi University Department of Mathematics The Chinese University of Hong Kong 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2003年第46卷第2期

页      面：176-186页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work was supported by a research grant of Shanxi Province for the first author and partially supported by a fund of UGC(HK) for the second author (Grant No. 2160126  1999/2000) 

主　　题：p-nilpotent groups, minimal subgroups, formation. 

摘      要：We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K ofG such that G = HK and H ∩K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotentif G is S4-free and every minimal subgroup of P ∩ GN is c-supplemented in NG(P), and when p = 2 P isquaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of *** some applications of this result, some known results are generalized.