Abstract
Let G be a finite group. The prime graph of G is denoted by Γ(G). The main result we prove is as follows: If G is a finite group such that Γ(G) = Γ(L 10(2)) then G/O 2(G) is isomorphic to L 10(2). In fact we obtain the first example of a finite group with the connected prime graph which is quasirecognizable by its prime graph. As a consequence of this result we can give a new proof for the fact that the simple group L 10(2) is uniquely determined by the set of its element orders.
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Original Russian Text Copyright © 2009 Khosravi Behrooz
The author was supported in part by the Institute for Studies in Theoretical Physics and Mathematics (IPM) (Grant 87200022).
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Tehran. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 446–452, March–April, 2009.
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Khosravi, B. Quasirecognition by prime graph of L 10(2). Sib Math J 50, 355–359 (2009). https://doi.org/10.1007/s11202-009-0040-5
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DOI: https://doi.org/10.1007/s11202-009-0040-5