| 几则有限群可解的条件 |
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| 引用本文： | 王俊新.几则有限群可解的条件[J].山东大学学报(理学版),2009,44(8):35-38. |
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| 作者姓名： | 王俊新 |
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| 作者单位： | 山西财经大学数学系; |
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| 基金项目： | 国家自然科学基金资助项目(10771132);;山西省高校科技项目(20081022) |
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| 摘 要： | 研究了子群的半覆盖远离性质与群的可解性之间的关系,得到了几则有限群可解的充要条件。主要结果为:有限群G可解当且仅当对G的每个极大子群M,或者M是G的半覆盖远离子 群,或者M存在可解的极大完备C,使得C是G的半覆盖远离子群。
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| 关 键 词： | 极大子群 半覆盖远离性 极大完备 可解群 |
| 收稿时间： | 2009-02-23 |
Some conditions for finite groups to be solvable |
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| WANG Jun-xin.Some conditions for finite groups to be solvable[J].Journal of Shandong University,2009,44(8):35-38. |
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| Authors: | WANG Jun-xin |
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| Institution: | Department of Mathematics;Shanxi University of Finance and Economics;Taiyuan 030031;Shanxi;China |
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| Abstract: | The relationships between the semi cover-avoiding property of subgroups and the solvability of groups are investigated.As an application,some sufficient and necessary conditions for finite groups to be solvable are obtained.It is proved that a finite group G is solvable if and only if for every maximal subgroup M of G,either M is semi cover-avoiding in G,or M has a solvable maximal completion C such that C is semi cover-avoiding in G. |
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| Keywords: | maximal subgroup semicover-avoiding property maximal completion solvable group |
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