| 极大子群的S-完备 |
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| 引用本文： | 唐曾林,梅汉飞. 极大子群的S-完备[J]. 湖南文理学院学报(自然科学版), 2007, 19(1): 22-24 |
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| 作者姓名： | 唐曾林 梅汉飞 |
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| 作者单位： | 湖南文理学院数学系,湖南,常德,415000;湖南文理学院数学系,湖南,常德,415000 |
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| 基金项目： | 湖南文理学院校科研和教改项目 |
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| 摘 要： | M是有限群G的一个给定极大子群,如果G的子群C不包含在M中,但是C的每个G-不变真子群都被M包含,那么就称C是M的一个完备。如果完备C同时还满足下列条件:或者C=D,或者C是子群D的一个极大子群,其中D不是M的完备,则称C是M的一个S-完备.利用极大子群的S-完备刻画了有限可解群.
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| 关 键 词： | 有限群 极大子群 可解群 |
| 文章编号： | 1672-6146（2007）01-0022-03 |
| 收稿时间： | 2006-10-18 |
| 修稿时间： | 2006-10-18 |
On s-Completion for Maximal Subgroups |
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| TANG Zeng-lin,MEI Han-fei. On s-Completion for Maximal Subgroups[J]. Journal of Hunan University of Arts and Science:Natural Science Edition, 2007, 19(1): 22-24 |
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| Authors: | TANG Zeng-lin MEI Han-fei |
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| Abstract: | For a given maximal subgroup M of a finite group G, a subgroup C of G is said to be a completion of M in G if C is not contained in M while every G-invariant proper subgroup of C is contained in M. An s-completion C of M is a completion satisfying the following condition: either C=G or there exists a subgroup D of G, which is not a completion of M such that D contains C as a maximal subgroup. In this paper, the finite solvable groups are characterized by using s-completions of maximal subgroups. |
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| Keywords: | Finite group maximal subgroup solvable group |
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