Quasirecognizability by the Set of Element Orders for Groups 3D4(q) and F4(q), for q Odd |
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| Authors: | O. A. Alekseeva and A. S. Kondratiev |
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| Affiliation: | (1) Chelyabinsk Humanitarian Institute, Voroshilova 8, Chelyabinsk, 454014, Russia;(2) Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, S. Kovalevskaya, 16, Ekaterinburg, 620066, Russia |
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| Abstract: | It is proved that if L is one of the simple groups 3D4(q) or F4(q), where q is odd, and G is a finite group with the set of element orders as in L, then the derived subgroup of G/F(G) is isomorphic to L and the factor group G/G′ is a cyclic {2, 3}-group. __________ Translated from Algebra i Logika, Vol. 44, No. 5, pp. 517–539, September–October, 2005. Supported by RFBR grant No. 04-01-00463. |
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| Keywords: | finite group simple group set of element orders quasirecognizability prime graph |
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