Abstract
The degrees of the irreducible characters of the Suzuki 2-groupsA(m,ϕ) are described. Assume that the order of an automorphism ϕ of the fieldGF (2 m) isk>1,G=A(m,ϕ), and cd (G) is the set of degrees of the irreducible characters ofG. Ifk is odd, then cd(G)={1, 2(m−m/k)/2}, and ifk=2, then cd(G)={1, 2 m/2 }. Ifk is even andk≠2 then cd(G)={1,2 m/2, 2m/2−m/k }, and the groupG has (2 m −1)2 m/k/(2m/k+1) characters of degree2 m/2 and (2m−1)22m/k/(2m/k+1) characters of degree 2m/2−m/k.
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References
B. Huppert and N. Blackburn,Finite Groups II, Springer, Berlin-Heidelberg-New York (1982).
A. Hanaki, “A condition on lengths of conjugacy classes and character degrees,”Osaka J. Math.,33, 207–216 (1996).
Ya. G. Berkovich, “A generalization of theorems of P. Hall and N. Blackburn and their application to nonregularp-groups,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],35, No. 4, 800–830 (1971).
A. I. Starostin, “Finite 2-groups with a cyclic Frattini subgroup,” in:Proceedings of the Institute of Mathematics and Mechanics [in Russian], Vol. 3, Ural Division of the Russian Academy of Sciences, Ekaterinburg (1995), pp. 60–64.
Ya. G. Berkovich and E. M. Zhmud,Characters of Finite Groups 1, Vol. 172, Transl. Math. Monographs, Amer. Math. Soc., Providence (R.I.) (1997).
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Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 258–263, August, 1999.
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Sagirov, I.A. Degrees of irreducible characters of the suzuki 2-groups. Math Notes 66, 203–207 (1999). https://doi.org/10.1007/BF02674878
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DOI: https://doi.org/10.1007/BF02674878