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

Article 8, Volume 38, Number 3, September 2012, Page 647-668  XML PDF (173 K)
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
Main Subjects
20-XX Group theory and generalizations
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