| 引用本文： |
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唐曾林,钟祥贵,黄雨星.有限可解群的CI-截刻画[J].广西科学,2007,14(3):196-199. [点击复制]
- TANG Zeng-lin,ZHONG Xiang-gui,HUANG Yu-xing.On the Solvability of Finite Groups Based on CI-section[J].Guangxi Sciences,2007,14(3):196-199. [点击复制]
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| 摘要: |
| 利用极大子群的CI-截定义,得到有限可解群的新刻画:(1)有限群G可解的充分必要条件是G中存在可解极大子群M∈Fs(G),使Sec(M)=1;(2)有限群G可解的充分必要条件是G中指数既非素数也非素数平方的极大子群M之Sec(M)为幂零群.推广了几个已知的重要结果. |
| 关键词: 有限群 极大子群 CI-截 可解群 |
| DOI： |
| 投稿时间：2006-08-07修订日期：2007-02-05 |
| 基金项目:湖南文理学院重点科研项目(JJZD0701);广西科学基金项目(0575050)资助 |
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| On the Solvability of Finite Groups Based on CI-section |
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TANG Zeng-lin1, ZHONG Xiang-gui2, HUANG Yu-xing1
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| (1.Department of Mathematis, Hunan University of Arts and Science, Changde, Hunan, 415000, China;2.Department of Mathematics, Guangxi Normal University, Guilin, Guangxi, 541004, China) |
| Abstract: |
| Some new characterizations of solvable finite groups are obtained using the concept of CI-section.They are (1)a group G is solvable if and only if there exists a solvable maximal subgroup M∈Fs (G) such that Sec (M)=1; (2)a group G is solvable if and only if Sec (M) is nilpotent for all maximal subgroups M of G such that|G:M|≠p, p2 where p is a prime divisor of |G|.Some previous results are generalized. |
| Key words: finite group maximal subgroup CI-section solvable group |
