| 关于极小子群的中心化子 |
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| 引用本文： | 杜妮. 关于极小子群的中心化子[J]. 厦门大学学报(自然科学版), 2002, 41(1): 13-16 |
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| 作者姓名： | 杜妮 |
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| 作者单位： | 厦门大学数学系,福建,厦门,361005 |
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| 摘 要： | 子群的中心化子对群的结构有很强的控制作用。称有限群G为PNC群，如果G的每个极小子群X均满足CG（X）＝NG（X）。首先证明了PNC群是介于幂零群与2－闭群之间的一类可解群。其次，考虑极小子群的中心化子与群的可解性的关系，给出了群可解性的若干充分条件。
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| 关 键 词： | 有限群 可解群 极小子群 中心化子 PNC群 幂零群 2－闭群 超可解群 |
| 文章编号： | 0438-0479(2002)01-0013-04 |
| 修稿时间： | 2000-10-26 |
On the Centralizers of the Minimal Subgroups of Finite Groups |
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| DU Ni. On the Centralizers of the Minimal Subgroups of Finite Groups[J]. Journal of Xiamen University(Natural Science), 2002, 41(1): 13-16 |
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| Authors: | DU Ni |
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| Abstract: | It's well known that the properties of the centralizers of subgroups of a finite group have a great influence on the structure of the group. If, for any minimal subgroup X of G, C G(X)=N G(X), G is called a PNC group. Firstly, we prove that PNC groups are solvable groups whose properties are between nilpotent groups and 2-closed groups. Secondly, we investigate the relationship between the centralizers of minimal subgroups and the solvability of a finite group. Some new sufficient conditions about the solvability of finite groups are obtained. |
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| Keywords: | finite group solvable group minimal subgroup centralizer |
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