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  • 1 Shahid Beheshti Univ. Dept. of Math., Faculty of Math. Sci. Evin, Tehran 19838 Iran
  • 2 Amirkabir University of Technology (Tehran Polytechnic) Dept. of Pure Math., Faculty of Math. and Computer Sci. 424, Hafez Ave. Tehran 15914 Iran
  • 3 Institute for Studies in Theoretical Physics and Mathematics (IPM) Tehran Iran
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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 [5] 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)). As a consequence of our results we prove that if p > 11 is a prime number and p ≢ 1 (mod 12), then PSL(2, p) is uniquely determined by its prime graph and so these groups are characterizable by their prime graph.

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