2-Recognizability by prime graph of PSL(2, p2) |
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Authors: | A. Khosravi B. Khosravi |
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Affiliation: | (1) University for Teacher Education, Tehran, Iran;(2) Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran;(3) Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran |
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Abstract: | Let G be a finite group and let Γ(G) be the prime graph of G. Assume p prime. We determine the finite groups G such that Γ(G) = Γ(PSL(2, p 2)) and prove that if p ≠ 2, 3, 7 is a prime then k(Γ(PSL(2, p 2))) = 2. We infer that if G is a finite group satisfying |G| = |PSL(2, p 2)| and Γ(G) = Γ(PSL(2, p 2)) then G ? PSL(2, p 2). This enables us to give new proofs for some theorems; e.g., a conjecture of W. Shi and J. Bi. Some applications are also considered of this result to the problem of recognition of finite groups by element orders. |
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Keywords: | simple group prime graph element order linear group |
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