On n-centralizer CA-groups

2020/11/10 by Mohammad A. Iranmanesh, Iranmanesh, Mohammad A., Mohammad Hossein Zareian +1
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2011.05058

openalex publication_date 2020/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite non-abelian group and m=|G|/|Z(G)|. In this paper we investigate m-centralizer group G with cyclic center and we will prove that if G is a finite non-abelian m-centralizer CA-group, then there exists an integer r>1 such that m=2^r. It is also prove that if G is an m-centralizer non-abelian finite group which is not a CA-group and its derived subgroup G' is of order 2, then there exists an integer s>1 such that m=2^2s.

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