Counting Centralizers of a Finite Group with an Application in Constructing the Commuting Conjugacy Class Graph

2021/01/22 by Али Реза Ашрафи, Ashrafi, A. R., Mohammad Ali Salahshour +1
Computer Science · Engineering · Mathematics · #20C15 (Primary) 20D15 (Secondary) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2101.09030

openalex publication_date 2021/01/22 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28

Abstract

The set of all centralizers of elements in a finite group G is denoted by Cent(G) and G is called n-centralizer if |Cent(G)| = n. In this paper, the structure of centralizers in a non-abelian finite group G with this property that (G)/(Z(G)) ≅ Z_p² \rtimes Z_p² is obtained. As a consequence, it is proved that such a group has exactly [(p+1)²+1] element centralizers and the structure of the commuting conjugacy class graph of G is completely determined.

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