| 张翠,史江涛,施武杰.交错群和对称群的一个新刻画[J].数学年刊A辑,2009,30(2):281~290 |
| 交错群和对称群的一个新刻画 |
| A New Characterization of Alternating Group and Symmetric Group |
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| DOI： |
| 中文关键词: 极大子群 共轭类型 单群 交错群 对称群 |
| 英文关键词:Maximal subgroup, The type of conjugacy classes, Simple group,
Alternating group, Symmetric group |
| 基金项目:国家自然科学基金，Agencija za raziskovalno dejavnost RepublikeSlovenia;re-search program P1-0285，高等学校博士学科点专项科研基金 |
| Author Name | Affiliation | E-mail | | ZHANG Cui | School of Science, Beijing Jiaotong University, Beijing 100044, China
Uni-
versity of Primorska, Primorska Institute of Natural Sciences and Technology,
Muzejski trg 2, 6000 Koper, Slovenia | 06118307@bjtu.edu.cn | | SHI Jiangtao | School of Mathematical Sciences, Suzhou University, Suzhou 215006, Jiangsu,
China. | shijt2005@163.com | | SHI Wujie | School of Mathematical Sciences, Suzhou University, Suzhou 215006, Jiangsu,
China. | wjshi@suda.edu.cn |
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| 中文摘要: |
| MT(G)=(m1,m2,…,mk)称为G的极大子群共轭类型,其中m1≤m2≤…≤mk,表示G有k个极大子群共轭类,并且第I个共轭类类长为mI.利用极大子群共轭类型给出全部交错群和部分对称群的一个新刻个画. |
| 英文摘要: |
| MT (G) = (m1,m2, .... ,mk) is called the type of conjugacy classes of maximal
subgroups of finite group G, where m1 <= m2 6<=....<= mk, which implies that G has exactly
k classes of conjugate maximal subgroups, and the class length of the i-th conjugacy class is
mi. This paper gives a new characterization of all alternating groups and some symmetric
groups by the type of conjugacy classes of maximal subgroups. |
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