Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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ON FINITE GROUPS WITH A CERTAIN NUMBER OF CENTRALIZERS

  • REZA ASHRAFI ALI (Department of Mathematics, Faculty of Science, University of Kashan) ;
  • TAERI BIJAN (Department of Mathematics, Isfahan University of Technology)
  • 발행 : 2005.01.01

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초록

Let G be a finite group and $\#$Cent(G) denote the number of centralizers of its elements. G is called n-centralizer if $\#$Cent(G) = n, and primitive n-centralizer if $\#$Cent(G) = $\#$Cent($\frac{G}{Z(G)}$) = n. In this paper we investigate the structure of finite groups with at most 21 element centralizers. We prove that such a group is solvable and if G is a finite group such that G/Z(G)$\simeq$$A_5$, then $\#$Cent(G) = 22 or 32. Moreover, we prove that As is the only finite simple group with 22 centralizers. Therefore we obtain a characterization of As in terms of the number of centralizers

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