| 引用本文： |
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李世荣,周龙桥,农国平,何俊.有限可解群的新刻画[J].广西科学,2008,15(4):330-333,337. [点击复制]
- LI Shi-rong,ZHOU Long-qiao,NONG Guo-ping,HE Jun.New Characterizations of Finite Solvable Groups[J].Guangxi Sciences,2008,15(4):330-333,337. [点击复制]
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| 摘要: |
| 在文献[3]的基础上,给出有限群极大子群的CI-截的3个性质,并得到有限群可解的3种新刻画:设G是有限群,如果G在Fs(G)中的极大子群的CI-截同构,则G可解;若p是|G|的一个素因子,对于群G的极大子群M∈Fps(G),M的CI-截的阶都是qarb,则G可解,其中q,r是两个不同于p的固定素数;设H是群G的S-拟正规子群,如果对于G的每个极大子群M,满足H⊈M时,M的CI-截幂零,则H可解. |
| 关键词: 可解群 极大子群 CI-截 |
| DOI： |
| 投稿时间：2008-05-23 |
| 基金项目: |
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| New Characterizations of Finite Solvable Groups |
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LI Shi-rong, ZHOU Long-qiao, NONG Guo-ping, HE Jun
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| (College of Mathematics and Information Sciences, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| Three pieces of properties of CI-section on maximal subgrop of finite group are given under reference [3], and some new characterizations of solvable finite groups are obtained using the concept of CI-section:let G be a finite group, if CI-sections of all maximal subgroups of {Fs (G)are isomorphic, then G is solvable;let p be a prime divisor of |G| and M be a maximal subgroup of G, if M∈Fps (G)such that |Sec (M)|=qarb, where q and r are two distinct primes and different from p, then G is solvable;let H be an S-quasinormal subgroup of G. If for each maximal subgroup M of G with H⊈M the CI-section of M is nilpotent, then H is solvable. |
| Key words: solvable group maximal subgroup CI-section |
