Finite Nonsolvable Groups in Which Only Two Nonlinear Irreducible Characters Have Equal Degrees

AbstractY. Berkovichet al.[Proc. Amer. Math. Soc.115(1992), 955–959] classified finite groups in which the degrees of the nonlinear irreducible characters are distinct. Theorem 24.7 from [Y. Berkovich,J. Algebra184(1996), 584–603] contains the classification of solvable groups in which only two nonlinear irreducible characters have equal degrees (D1-groups). In this paper we obtain the classification of nonsolvableD1-groups, completing the classification ofD1-groups. Our proof depends on the classification of finite simple groups. The results of the important paper [Illinois J. Math.33, No. 1 (1988), 103–131] on rational simple groups play a key role as well