| 关于C-正规子群与有限群的可解性 |
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| 引用本文： | 刘国刚.关于C-正规子群与有限群的可解性[J].华南理工大学学报(自然科学版),2004,32(11):93-96. |
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| 作者姓名： | 刘国刚 |
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| 作者单位： | 中山大学,数学与计算科学学院,广东,广州,510275 |
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| 基金项目： | 国家自然科学基金资助项目 (10 16 10 0 1)，广东省自然科学基金资助项目 (2 0 0 0 0 86 4 ) |
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| 摘 要： | 若有限群G的一些子群(极大子群，Sylow子群及其子群)是群G的C-正规子群，则得到有限群G可解的一些充分条件和充要条件，群G是否可解可以通过它的这些子群是否为C-正规子群来判断，在证明过程中，对群的阶采用极小阶反例的方法即归纳法与反证法相结合的方法。另外，还引入了一个新的子群的集合L(G)，即不包含群G的导群的极大子群。
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| 关 键 词： | 有限群 可解群 极大子群 C-正规子群 |
| 文章编号： | 1000-565X(2004)11-0093-04 |
| 修稿时间： | 2003年6月2日 |
C-normal Subgroups and Solvability of Finite Groups |
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| Liu Guo-gang.C-normal Subgroups and Solvability of Finite Groups[J].Journal of South China University of Technology(Natural Science Edition),2004,32(11):93-96. |
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| Authors: | Liu Guo-gang |
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| Abstract: | It is proved in this paper, if some subgroups of the finite group G, such as the maximal subgroup, Sylow subgroup and its subgroups, are also C-normal subgroups of group G, some sufficient conditions as well as necessary and sufficient conditions for the solvability of group G can be obtained. By determining whether its subgroups are C-normal subgroups, the solvability of group G can be determined. In the proof, the method of contradiction of the extreme minimal rank of group G is adopted. This method is a combination of induction and reduction to absurdity. Besides, a new subgruop set L(G), that is, the maximal subgroups excluding the guided group of G is introduced into the proof. |
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| Keywords: | finite group solvable group maximal subgroup C-normal subgroup |
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