## “School of Mathematics”

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Paper   IPM / M / 8467
 School of Mathematics Title: On the prime graph of PSL(2,P) where P > 3 is a prime number Author(s): Behr. Khosravi (Joint with Behn. Khosravi and Bah. Khosravi) Status: Published Journal: Acta Math. Hungar. Vol.: 116 Year: 2007 Pages: 295-307 Supported by: IPM
Abstract:
Let G be a finite group. We define the prime graph Γ(G) as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge if there is an element in G of order pq. Recently M. Hagie in (Hagie, M. (2003), The prime graph of a sporadic simple group, Comm. Algebra, 31: 4405-4424) determined finite groups G satisfying Γ(G)=Γ(S), where S is a sporadic simple group. Let p > 3 be a prime number. In this paper we determine finite groups G such that Γ(G)=Γ(PSL(2,p)). ALso is prove that if p > 11 and p\not ≡ 1 (mod 12), then PSL(2,p) is uniquely determined by its prime graph. As a consequence of our results we can give positive answer to a conjecture of W.Shi and J. Bi for the group PSL(2,p).