A New Characterization of PGL(2, p) by Its Noncommuting Graph
نویسنده
چکیده
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 6= 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 J. G. Thompson and another conjecture of W. Shi and J. Bi for the group PGL(2, p) are proved.
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