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Degrees of irreducible characters of the suzuki 2-groups
Authors:I A Sagirov
Institution:(1) P. G. Demidov Yaroslavl State University, USA
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 , 2 m/2−m/k }, and the groupG has (2 m −1)2 m/k /(2 m/k +1) characters of degree2 m/2 and (2m−1)22m/k/(2m/k+1) characters of degree 2m/2−m/k. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 258–263, August, 1999.
Keywords:Suzuki 2-group  irreducible character  degree of a group character  nonprincipal character  Frattini subgroup  extraspecial group  semi-Abelian group
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