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

Foroudi Ghasemabadi, M.; Iranmanesh, A.; Ahanjideh, N.

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

Document Type : Research Paper

Authors

M. Foroudi Ghasemabadi ¹

A. Iranmanesh ¹

N. Ahanjideh ²

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.

Keywords

Prime graph

classification of finite simple groups

recognition

spectrum

Subjects