Commuting graph of CA−groups

• Torktaz, Mehdi ^[2] ; Ashrafi, Ali Reza ^[1]
  1. [1] University of Kashan

     University of Kashan

     Irán

     
  2. [2] Unversity of Kashan.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 1, 2023, págs. 1-17
• Idioma: inglés
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• Resumen

  • A group G is called a CA−group, if all the element centralizers of G are abelian and the commuting graph of G with respect to a subset A of G, denoted by Γ(G, A), is a simple undirected graph with vertex set A and two distinct vertices a and b are adjacent if and only if ab = ba. The aim of this paper is to generalize results of a recently published paper of F. Ali, M. Salman and S. Huang [On the commuting graph of dihedral group, Comm. Algebra 44 (6) (2016) 2389—2401] to the case that G is an CA−group.