| 剩余有限minimax可解群的自同构 |
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| 引用本文： | 徐涛,刘合国.剩余有限minimax可解群的自同构[J].数学学报,2017,60(4):681-688. |
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| 作者姓名： | 徐涛 刘合国 |
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| 作者单位： | 1. 河北工程大学数理学院 邯郸 056038;
2. 湖北大学数学与统计学学院 武汉 430062 |
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| 基金项目： | 国家自然科学基金资助项目（11371124，11626078）；河北省教育厅青年基金（QN2016184）和河北工程大学研究生教育教学改革项目（161290140004） |
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| 摘 要： | 设G是剩余有限minimax可解群,α是G的自同构且φ:G→G(g→g,α])是满射,则有以下结果:(1)当α~p=1时,G是幂零类不超过h(p)的幂零群的有限扩张,其中h(p)是只与p有关的函数;(2)当α~4=1时,G存在一个指数有限的特征子群H,使得H″≤Z(H)和C_H(α~2)是Abel群.并且C_G(α~2)和G/G,α~2]都是Abel群的有限扩张.
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| 关 键 词： | 剩余有限 minimax可解群 正则自同构 自同构 |
On Automorphisms of Residually Finite Minimax Soluble Groups |
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| Tao XU,He Guo LIU.On Automorphisms of Residually Finite Minimax Soluble Groups[J].Acta Mathematica Sinica,2017,60(4):681-688. |
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| Authors: | Tao XU He Guo LIU |
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| Affiliation: | 1. Department of Science, Hebei University of Engineering, Handan 056038, P. R. China;
2. College of Mathematics and Statistics, Hubei University, Wuhan 430062, P. R. China |
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| Abstract: | Let G be a residually finite minimax soluble group and α an automorphism of G.If the map φ:G → G defined by gφ=g,α]is surjective,then the following hold:(1) When αp=1,G is (nilpotent of class at most h(p))-by-finite,where h(p) is a function depending only on p;(2) When α4=1,G contains a characteristic subgroup H of finite index such that the second derived subgroup H"is included in the centre of H and CH(α2) is abelian.Both CG(α2) and G/G,α2]are abelian-by-finite. |
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| Keywords: | residually finite minimax soluble group regular automorphism automorphism |
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