A cohomological property of semi-abelian p-groups

2014/06/20 by Mohammed T. Benmoussa, Benmoussa, Mohammed T., Yassine Guerboussa +1
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1406.5397

openalex publication_date 2014/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a cohomological property for a class of finite p-groups introduced earlier by M. Y. Xu, which we call semi-abelian p-groups. This result implies that a semi-abelian p-group has non-inner automorphisms of order p, which settles a longstanding problem for this class. We answer also, independetly, an old question of M. Y. Xu about the power structure of semi-abelian p-groups.

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