On central automorphisms of groups and nilpotent rings

2012/12/25 by Yassine Guerboussa, Guerboussa, Yassine, Bounabi Daoud +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1212.6067

openalex publication_date 2012/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group. The central automorphism group Aut_c(G) of G is the centralizer of Inn(G) the subgroup of Aut(G) of inner automorphisms. There is a one to one map σ↦ h_σ from the set Aut_c(G) onto the set Hom(G,Z(G)) of homomorphisms from G onto its center, with h_σ(x)=x^-1 σ(x). This map can be used to obtain informations about the size of Aut_c(G), and also about its structure in some special cases. In this paper we see how to use it to obtain informations about the structure of Aut_c(G) in the general case. The notion of the adjoint group of a ring is the main tool in our approach.

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• Some automorphism groups of finite p-groups
• A module-theoretic approach to abelian automorphism groups

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