有限ATI-群的类保持Coleman自同构 |
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引用本文: | 海进科,李正兴. 有限ATI-群的类保持Coleman自同构[J]. 数学学报, 2010, 53(5): 891-896 |
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作者姓名: | 海进科 李正兴 |
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作者单位: | 青岛大学数学科学学院 青岛 266071 |
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基金项目: | 国家自然科学基金资助项目(10771132)山东省自然科学基金资助项目(Y2008A03)及山东省教育厅基金资助项目(J07YH06) |
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摘 要: | 设G是一个有限群,对G的任意阿贝尔子群A及任意g∈G,若A∩A~g=1或A,则称G为一个ATI-群.本文证明了,对任意p∈τ(G),如果ATI-群G的一个p-方幂阶类保持自同构在G的任意Sylow子群上的限制等于G的某个内自同构的限制,则它必定是一个内自同构.作为该结果的一个直接推论,我们也证明了有限ATI-群G有正规化性质.
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关 键 词: | 自同构群 类保持自同构及Coleman自同构 ATI-群 |
收稿时间: | 2009-05-25 |
修稿时间: | 2010-03-16 |
Class-Preserving Coleman Automorphisms of Finite ATI-Groups |
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Affiliation: | School of Mathematics, Qingdao University, Qingdao 266071, P. R. China |
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Abstract: | A finite group G is called an ATI-group if for any abelian subgroup A of G, A∩Ag=1 or A for all g∈G. In this paper, it is shown that a class-preserving automorphism of an ATI-group G of p-power order whose restriction to any Sylow subgroup of G is equal to the restriction of some inner automorphism of G is necessarily an inner automorphism. As an immediate consequence, we obtain that the normalizer property holds for finite ATI-groups. |
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Keywords: | automorphism groups class-preserving automorphisms and Coleman automorphisms ATI-groups |
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