On p-nilpotency and minimal subgroups of finite groups  

作　　者：郭秀云 K.P.Shum 

机构地区：[1]Department of Mathematics, Shanxi University [2]Department of Mathematics, The Chinese University of Hong Kong

出　　处：《Science China Mathematics》2003年第2期176-186,共11页中国科学：数学（英文版）

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).

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 G.As some applications of this result, some known results are generalized.We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ? core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S 4-free and every minimal subgroup of P ∩ G N is c-supplemented in N G (P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized.

关 键 词：P-NILPOTENT groups  MINIMAL subgroups  formation. 

分 类 号：O152[理学—数学]