Abstract
Let G be a finite group. The main result of this paper is as follows: If G is a finite group, such that Γ(G) = Γ(2G2(q)), where q = 32n+1 for some n ≥ 1, then G has a (unique) nonabelian composition factor isomorphic to 2 G 2(q). We infer that if G is a finite group satisfying |G| = |2 G 2(q)| and Γ(G) = Γ (2 G 2(q)) then G ≅ = 2 G 2(q). This enables us to give new proofs for some theorems; e.g., a conjecture of W. Shi and J. Bi. Some applications of this result are also considered to the problem of recognition by element orders of finite groups.
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Original Russian Text Copyright © 2007 Khosravi A. and Khosravi B.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 3, pp. 707–716, May–June, 2007.
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Khosravi, A., Khosravi, B. Quasirecognition by prime graph of the simple group 2 G 2(q). Sib Math J 48, 570–577 (2007). https://doi.org/10.1007/s11202-007-0059-4
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DOI: https://doi.org/10.1007/s11202-007-0059-4