Abstract
The spectrum of a finite group G is the set of the orders of elements of G. In the present article, we obtain an arithmetical description of the spectra of finite symplectic and orthogonal groups. In particular, we describe the spectra of finite simple groups in these two classes.
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References
M. Aschbacher, Finite Group Theory, vol. 10 of Cambridge Studies in Advanced Mathematics (Cambridge University Press, Cambridge, 1986).
A. A. Buturlakin, “Spectra of finite linear and unitary groups,” Algebra i Logika 47(2), 157–173 (2008) [Algebra and Logic 47 (2), 91–99 (2008)].
A. A. Buturlakin and M. A. Grechkoseeva, “The cyclic structure of maximal tori of the finite classical groups,” Algebra i Logika 46(2), 129–156 (2007) [Algebra and Logic 46 (2), 73–89 (2007)].
R.W. Carter, Simple Groups of Lie Type, vol. 28 of Pure and Applied Mathematics (Wiley, London, 1972).
R.W. Carter, “Centralizers of semisimple elements in finite groups of Lie type,” Proc. London Math. Soc. (3) 37(3), 491–507 (1978).
R.W. Carter, “Centralizers of semisimple elements in the finite classical groups,” Proc. London Math. Soc. (3) 42(1), 1–41 (1981).
R. W. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters (Wiley, New York, 1985).
R. Steinberg, Endomorphisms of Linear Algebraic Groups, Mem. Amer.Math. Soc. 80(Amer.Math. Soc., Providence, RI, 1968).
D.M. Testerman, “A 1-Type overgroups of elements of order p in semisimple algebraic groups and the associated finite groups,” J. Algebra 177(1), 34–76 (1995).
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Original Russian Text © A. A. Buturlakin, 2010, published in Matematicheskie Trudy, 2010, Vol. 13, No. 2, pp. 33–83.
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Buturlakin, A.A. Spectra of finite symplectic and orthogonal groups. Sib. Adv. Math. 21, 176–210 (2011). https://doi.org/10.3103/S1055134411030035
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DOI: https://doi.org/10.3103/S1055134411030035