A New Characterization of PGL(2, p) by its Noncommuting Graph

作者：Khosravi B^*; Khatami M

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2011, 34(3): 665-674.

• Noncommuting graph
• prime graph
• order components
• characterization
• finite group

Let G be a finite non-abelian group. The noncommuting graph of G is denoted by del(C) and is defined as follows: the vertex set of del(G) is G\Z (G) and two vertices x and y are adjacent if and only if xy not equal yx. Let p be a prime number. In this paper, it is proved that the almost simple group PG L(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.

• 出版日期2011