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

Journal Archive

	2-recognizability of the simple groups $B_n(3)$ and $C_n(3)$ by prime graph
Articles in Press, Accepted Manuscript , Available Online from 23 December 2011
Document Type: Research Paper
Authors
¹Ali Iranmanesh ; ¹Mahnaz Foroudi Ghasemabadi; ²Neda Ahanjideh
¹Tarbiat Modares University
²University 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
Main Subjects
20-XX Group theory and generalizations
Statistics Article View: 63