| 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). |
|
| Hits: 3145 |
| Download times: 3032 |
| 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 |
| View Full Text View/Add Comment |
