Title of article :
A New Characterization of PGL(2,p) by its Noncommuting Graph
Author/Authors :
Khosravi, B. amirkabir university of technology - Faculty of Mathematics and Computer Science - Department of Pure Mathematics, تهران, ايران , Khosravi, B. Institute for Research in Fundamental Sciences (IPM) - School of Mathematics, ايران , Khatami, M. amirkabir university of technology - Faculty of Mathematics and Computer Science - Department of Pure Mathematics, تهران, ايران
Abstract :
Let G be a finite non-abelian group. The noncommuting graph of G is denoted by ∇(G) and is defined as follows: the vertex set of ∇(G) is G∖Z(G) and two vertices x and y are adjacent if and only if xy≠yx. Let p be a prime number. In this paper, it is proved that the almost simple group PGL(2,p) is uniquely determined by its noncommuting graph. As a consequence of our results the validity of a conjecture of Thompson and another conjecture of Shi and Bi for the group PGL(2,p) are proved.
Keywords :
Noncommuting graph , prime graph , order components , characterization , finite group
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
