Recognition of the Group O+10(2) from Its Spectrum
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We prove that if the set of orders of elements of a finite group G coincides with the set of orders of elements of the group D=O10+(2), then G is isomorphic to D. In other words, O10+(2) is recognizable from its spectrum.
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- 1.Mazurov V. D., “Recognition of the finite simple groups S 4(q) from their sets of element orders,” Algebra i Logika, 41, No. 2, 166–198 (2002).Google Scholar
- 2.Shi W. and Tang C. J., “A characterization of some orthogonal groups,” Prog. Nat. Sci., 7, No. 2, 155–162 (1997) 36, No. 1, 36-53 (1997).Google Scholar
- 4.Williams J. S., “Prime graph components of finite groups,” J. Algebra, 69, No. 2, 487–513 (1981).Google Scholar
- 5.Vasil'ev A. V., “Recognition of the groups S 4(q) from their element orders,” Algebra i Logika, 41, No. 2, 130–142 (2002).Google Scholar
- 6.Conway J. H., Curtis R. T., Norton S. P., and Wilson R. A., Atlas of Finite Groups, Clarendon Press, Oxford (1985).Google Scholar
- 7.Grechkoseeva M. A., “On minimal permutation representations of classical simple groups,” Sibirsk. Mat. Zh., 44, No. 3, 559–583 (2003).Google Scholar
- 8.Carter R. W., Simple Groups of Lie Type, John Wiley & Sons, London (1972).Google Scholar
- 9.Borel A., Carter R., Curtis C. W., Iwahori N., Springer T. A., and Steinberg R., Seminar on Algebraic Groups and Related Finite Groups, [Russian translation], Mir, Moscow (1973).Google Scholar