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On <Emphasis Type="Italic">p</Emphasis>-nilpotency and minimal subgroups of finite groups
Authors:Email author" target="_blank">Xiuyun?GuoEmail author  Email author" target="_blank">K?P?ShumEmail author
Institution:(1) Department of Mathematics, Shanxi University, 030006 Taiyuan, China;(2) Department of Mathematics, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China (SAR)
Abstract: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 HK ⩽ 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 PG 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.
Keywords:p-nilpotent groups  minimal subgroups  formation
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