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

✍ Scribed by Yakov Berkovich; Lev Kazarin

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 242 KB
• Volume: 184
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.0273

✦ Synopsis

Berkovich et al. Proc. Amer. Math. Soc. 115 1992 , 955᎐959 classified

finite groups in which the degrees of the nonlinear irreducible characters are distinct. w Ž . x Theorem 24.7 from Y. Berkovich, J. Algebra 184 1996 , 584᎐603 contains the classification of solvable groups in which only two nonlinear irreducible characters Ž . have equal degrees D -groups . In this paper we obtain the classification of 1 nonsolvable D -groups, completing the classification of D -groups. Our proof 1 1 depends on the classification of finite simple groups. The results of the important w Ž . x paper Illinois J. Math. 33, No. 1 1988 , 103᎐131 on rational simple groups play a key role as well.