Corrigendum to “Determining group structure from sets of irreducible character degrees” [J. Algebra 206 (1) (1998) 235–260]

On Finite Groups With Two Irreducible Character Degrees

Prime Divisors of Irreducible Character Degrees

Let G be a finite group. We denote by ρ(G) the set of primes which divide some character degrees of G and by σ(G) the largest number of distinct primes which divide a single character degree of G. We show that |ρ(G)| ≤ 2σ(G) + 1 when G is an almost simple group. For arbitrary finite groups G, we show that |ρ(G)| ≤ 2σ(G) + 1 provided that σ(G) ≤ 2.

on finite groups with two irreducible character degrees

1 F eb 1 99 7 IRREDUCIBLE CHARACTER DEGREES AND NORMAL SUBGROUPS

1. Introduction. Let G be a finite group and, as usual, write cd(G) to denote the set of degrees of the irreducible characters of G. This set of positive integers encodes a great deal of information about the structure of G, and we mention just a few of the many known results of this type. If G is nilpotent (or more generally, if G is an M-group), a result of K. Taketa asserts that the derived ...

Determining a Connected Split Reductive Group from Its Irreducible Representations

We show that a connected split reductive group G over a field of characteristic 0 is uniquely determined up to isomorphism by specifying a maximal torus T of G , the set of isomorphism classes of irreducible representations of G , and the character homomorphism from the Grothendieck ring of G to that of T .