FINITE NONSOLVABLE GROUPS IN WHICH ONLY 2 NONLINEAR IRREDUCIBLE CHARACTERS HAVE EQUAL DEGREES

Y. Berkovich et al. [Proc. Amer. Math. Soc. 115 (1992), 955-959] class ified finite groups in which the degrees of the nonlinear irreducible characters are distinct. Theorem 24.7 from [Y. Berkovich, J. Algebra 1 84 (1996), 584-603] contains the classification of solvable groups in which only two nonlinear irreducible characters have equal degrees (D- 1-groups). In this paper we obtain the classification of nonsolvable D -1-groups, completing the classification of D-1-groups. Our proof depe nds on the classification of finite simple groups. The results of the important paper [Illinois J. Math. 33, No. 1 (1988), 103-131] on ratio nal simple groups play a key role as well. (C) 1996 Academic Press, In c.