| 具有一个T．I．Sylow 2-子群的有限群的类保持Coleman自同构 |
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| 引用本文： | 海进科 Wang Yulei.具有一个T．I．Sylow 2-子群的有限群的类保持Coleman自同构[J].数学学报,2008,51(6):1115-111. |
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| 作者姓名： | 海进科 Wang Yulei |
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| 作者单位： | 青岛大学数学系 |
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| 摘 要： | 设G是一个有限群,它的Sylow 2-子群是T.I.集,证明了如果G的2的方幂阶类保持自同构在G任意的Sylow子群上的限制等于G的某个内自同构的限制,则它一定是一个内自同构.对这样的自同构的研究是由整群环的同构问题所引起的.
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| 关 键 词： | 自同构群 类保持自同构 Coleman自同构 |
| 收稿时间： | 2006-12-11 |
Class-Preserving Coleman Automorphisms of the Finite Group with a T.I. Sylow 2-Subgroup |
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| Institution: | Deptartment of Mathematics, Qingdao University, Qingdao 266071, P. R. China Deptartment of Mathematics, Qingdao University, Qingdao 266071, P. R. China |
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| Abstract: | Let $G$ be a finite group
whose Sylow $2$-subgroups are T.I. sets. It is shown that the class-preserving automorphism of
$G$ of order a power of $2$ whose restriction to any Sylow subgroup of $G$ equals the
restriction of some inner automorphism of $G$ is necessarily an inner automorphism.
Interest in such automorphisms has arisen from the study of the isomorphism problem for
integral group rings. |
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| Keywords: | automorphism group class-preserving automorphism Coleman automor-phism |
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