李正兴,海进科.二极大子群为TI-子群的有限群的类保持Coleman自同构[J].数学研究及应用,2013,33(2):241~245
二极大子群为TI-子群的有限群的类保持Coleman自同构
Class-Preserving Coleman Automorphisms of Finite Groups Whose Second Maximal Subgroups Are TI-Subgroups
投稿时间:2011-07-07  最后修改时间:2011-12-20
DOI:10.3770/j.issn:2095-2651.2013.02.011
中文关键词:  正规化子性质  Coleman自同构  类保持自同构.
英文关键词:normalizer property  Coleman automorphism  class-preserving automorphism.
基金项目:国家自然科学基金(Grant Nos.11171169; 11071155), 山东省博士基金(Grant No.BS2012SF003).
作者单位
李正兴 青岛大学数学科学学院, 山东 青岛 266071 
海进科 青岛大学数学科学学院, 山东 青岛 266071 
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中文摘要:
      设$H$是有限群$G$的一个子群,若对任意$g\in G$, $H\cap H^g=1$或者$H$,则称$H$为TI-子群. 设$G$是一个所有二极大子群为TI-子群的有限群,本文证明了$G$的每个类保持Coleman自同构是内自同构. 作为本结果的一个直接推论,得到了这样的群$G$有正规化子性质.
英文摘要:
      Recall that a subgroup $H$ of a finite group $G$ is called a TI-subgroup if $H\cap H^{g}=1$ or $H$ for each $g\in G$. Suppose that $G$ is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class-preserving Coleman automorphism of $G$ is an inner automorphism. As an immediate consequence of this result, we obtain that the normalizer property holds for $G$.
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