| 超可解群的几个充分条件 |
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| 引用本文： | 赵啸海.超可解群的几个充分条件[J].广西大学学报(自然科学版),2001,26(2):137-139. |
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| 作者姓名： | 赵啸海 |
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| 作者单位： | 广西广播电视大学理工部, |
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| 摘 要： | 设有限群G可解，G／N超可解，若N还满足下列条件之一，则G超可解：（1）N的极大子群在G中弱拟正规；（2）N＝G，且N的Sylow子群的正规化子的极大子群在G中弱拟正规；（3）N的Sylow子群的极大子群在G中弱拟正规；（4）N的Sylow子群的循环子群在G中弱拟正规。
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| 关 键 词： | 有限群 子群 可解群 超可解群 |
| 文章编号： | 1001-7445(2001)02-0137-03 |
| 修稿时间： | 2001年2月12日 |
Some sufficient conditions for a finite group to be supersolvable |
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| ZHAO Xiao-hai.Some sufficient conditions for a finite group to be supersolvable[J].Journal of Guangxi University(Natural Science Edition),2001,26(2):137-139. |
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| Authors: | ZHAO Xiao-hai |
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| Abstract: | Let G be solvable and G/N be supersolvable.If N satisfies one of the following conditions,then G is supersolvable.(1) All maximal subgroups of N are weakly quasinormal in G;(2) N=G and all maximal subgroups of N G(P) are weakly quasinormal in G, for every Sylow subgroup P of N; (3) all maximal subgroups of Sylow subgroups of N are weakly quasinormal in G;(4) all cyclic subgroups of Sylow subgroups of N are weakly quasinormal in G. |
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| Keywords: | finite group subgroup solvable group supersolvable group |
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