2-quasirecognizability  of the simple groups B_n(p) and C_n(p) by prime graph

Foroudi Ghasemabadi, Mahnaz; Iranmanesh, Ali

2-quasirecognizability of the simple groups B_n(p) and C_n(p) by prime graph

Document Type : Research Paper

Authors

Mahnaz Foroudi Ghasemabadi

Ali Iranmanesh

Tarbiat Modares University

Abstract

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

odd number. In this paper, we show that if $GK(G)=GK(B_n(p))$, where $ngeq 9$ and $pin

{3,5,7}$, then G has a unique nonabelian composition factor isomorphic to $B_n(p)$ or

$C_n(p)$ . As consequences of our result, $B_n(p)$ is quasirecognizable by its spectrum

and also by a new proof, the validity of a conjecture of W. J. Shi for $B_n(p)$

is obtained.

Keywords

Quasirecognition

Prime graph

simple group

element order

Subjects