| On p-nilpotency and minimal subgroups of finite groups |
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| 引用本文： | 郭秀云,K.P.Shum. On p-nilpotency and minimal subgroups of finite groups[J]. 中国科学A辑(英文版), 2003, 46(2). DOI: 10.1360/03ys9019 |
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| 作者姓名： | 郭秀云 K.P.Shum |
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| 作者单位： | Department of Mathematics，Shanxi University，Department of Mathematics，The Chinese University of Hong Kong Taiyuan 030006，China，Shatin，N. T.，Hong Kong，China (SAR) |
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| 基金项目： | 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). |
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| 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 n 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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On p-nilpotency and minimal subgroups of finite groups |
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| K.P.Shum. On p-nilpotency and minimal subgroups of finite groups[J]. Science in China(Mathematics), 2003, 46(2). DOI: 10.1360/03ys9019 |
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| Authors: | K.P.Shum |
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| Affiliation: | 1. Department of Mathematics, Shanxi University, Taiyuan 030006, China
2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China (SAR) |
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| Abstract: | 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. |
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| Keywords: | p-nilpotent groups minimal subgroups formation. |
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