A note on noninner automorphisms of order $p$ for finite $p$-groups of coclass 2

A. Abdollahi; S. M. Ghoraishi; B. Wilkens

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arXiv · 1306.2649

A note on noninner automorphisms of order $p$ for finite $p$-groups of coclass 2

A. Abdollahi·S. M. Ghoraishi·B. Wilkens

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Abstract

In this note, the existence of noninner automorphisms of order 2 for finite 2-groups of coclass 2 is proved. Combining our result with a recent one due to Y. Guerboussa and M. Reguiat (see arXiv:1301.0085), we prove that every finite $p$-group of coclass 2 has a noninner automorphism of order $p$ leaving the center elementwise fixed.

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A. Abdollahi, S. M. Ghoraishi, B. Wilkens. 2013-06-11. A note on noninner automorphisms of order $p$ for finite $p$-groups of coclass 2. https://arxiv.org/abs/1306.2649

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