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. |