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

2025/05/07 by Xuesong Ma, Wei Xu, Ma, Xuesong +1 · 1 citation
Mathematics · #20D15 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2505.04125

openalex publication_date 2025/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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(γ₃(G)G^p))\nleqslantγ₃(G)G^p, then G has a non-inner automorphism of order p.

Citations

• Quasi-powerful p-groups
• Non-inner automorphisms of order p in finite p-groups of coclass 3
• Powerful p-groups have noninner automorphisms of order p and some cohomology

Cited by

• On cohomologically Trivially modules over finite p-groups

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