Class-Preserving Coleman Automorphisms of Finite Groups Whose Second Maximal Subgroups Are TI-Subgroups
Received:July 07, 2011  Revised:December 20, 2011
Key Words: normalizer property   Coleman automorphism   class-preserving automorphism.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11171169; 11071155) and the Doctoral Foundation of Shandong Province (Grant No.BS2012SF003).
Author NameAffiliation
Zhengxing LI College of Mathematics, Qingdao University, Shandong 266071, P. R. China 
Jinke HAI College of Mathematics, Qingdao University, Shandong 266071, P. R. China 
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Abstract:
      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 $G$.
Citation:
DOI:10.3770/j.issn:2095-2651.2013.02.011
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