On p-nilpotency and minimal subgroups of finite groups

被引：0
作者：
Xiuyun Guo
K. P. Shum
机构：
[1] Shanxi University,Department of Mathematics
[2] The Chinese University of Hong Kong,Department of Mathematics
来源：
Science in China Series A: Mathematics | 2003年 / 46卷
关键词：
p-nilpotent groups; minimal subgroups; formation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 S4-free and every minimal subgroup of P ∩ GN is c-supplemented in NG(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.
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页码：176 / 186
页数：10
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