Finite Groups with a Pre-Fixed-Point-Free Power Automorphism |
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| Authors: | Junxin Wang Xiuyun Guo |
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| Institution: | 1. Department of Mathematics , Shanxi University of Finance and Economics , Taiyuan , China wangjunxin660712@163.com;3. Department of Mathematics , Shanghai University , Shanghai , China |
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| Abstract: | A power automorphism θ of a group G is said to be pre-fixed-point-free if CG(θ) is an elementary abelian 2-group. G is called an E-group if G has a pre-fixed-point-free power automorphism. In this paper, finite E-groups, together with all their pre-fixed-point-free power automorphisms, are completely determined. Moreover, a characteristic of finite abelian groups is given, which explains some known facts concerning power automorphisms. |
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| Keywords: | Minimal nonabelian groups Power automorphisms p-Groups |
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