On recognizability of some finite simple orthogonal groups by spectrum |
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| Authors: | O A Alekseeva A S Kondrat’ev |
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| Institution: | 1.Chelyabinsk Institute of Humanities,Chelyabinsk,Russia;2.Institute of Mathematics and Mechanics,Ural Division of the Russian Academy of Sciences,Yekaterinburg,Russia |
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| Abstract: | It is proved that, if G is a finite group that has the same set of element orders as the simple group D p (q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D p (q), the subgroup F(G) is equal to 1 for q = 5 and to O q (G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2. |
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