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arXiv · 2505.04125

Non-inner automorphisms of order $p$ in finite $p$-groups admitting cyclic center

Xuesong Ma·Wei Xu
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Abstract

Let $G$ be a finite non-abelian $p$-group admitting cyclic center and $p$ be an odd prime. In this paper, we prove that if $C_{G}(Z(\gamma_{3}(G)G^{p}))\nleqslant\gamma_{3}(G)G^{p}$, then $G$ has a non-inner automorphism of order $p$.

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Xuesong Ma, Wei Xu. 2025-05-07. Non-inner automorphisms of order $p$ in finite $p$-groups admitting cyclic center. https://arxiv.org/abs/2505.04125

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