2-recognizability of the simple groups $B_n(3)$ and $C_n(3)$ by prime graph

Document Type: Research Paper

Authors

1 Tarbiat Modares University

2 University of Shahre-kord

Abstract

Let $G$ be a finite group and let $GK(G)$ be the prime graph of $G$. We assume that

$ngeqslant 5 $ is an odd number. In this paper, we show that the simple groups

$B_n(3)$ and $C_n(3)$ are 2-recognizable by their prime graphs. As consequences of the

result, the characterizability of the groups $B_n(3)$ and $C_n(3)$ by their spectra and

by the set of orders of maximal abelian subgroups are obtained. Also, we can conclude

that the AAM's conjecture is true for the groups under study.

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Main Subjects



Volume 39, Issue 6
November and December 2013
Pages 1273-1281
  • Receive Date: 25 May 2011
  • Revise Date: 21 September 2011
  • Accept Date: 22 September 2011