Malaysian Journal of Mathematical Sciences, May 2018, Vol. 12, No. 2
Classification of Finite Simple Groups According to the Number of Centralizers
Foruzanfar, Z., Mostaghim, Z., and Rezaei, M.
Corresponding Email: mostaghim@iust.ac.ir
Received date: 2 November 2016
Accepted date: 21 January 2018
Abstract:
Let \(G\) be a finite group and \(\left |Cent(G)\right |\) be the number of distinct centralizers of its elements. \(G\) is called \(n-centralizer\) if \(\left |Cent(G)\right | = n\). In this paper, we classify all finite non-abelian simple groups \(G\) with \(\left |Cent(G)\right | \leq 100\).
Keywords: Finite group, n-centralizer group, simple group
