Primes Dividing Character Degrees and Character Orbit Sizes

ORBIT SIZES AND CHARACTER DEGREESThomas

The objective of this paper is to develop criteria that guarantee that a nite group G which acts faithfully on a vector space V possesses \many" orbits of diierent sizes. This has consequences on (classical and modular) character degrees of nite solvable groups.

Nonsolvable Groups with No Prime Dividing Three Character Degrees

Throughout this note, G will be a finite group, Irr(G) will be the set of irreducible characters of G, and cd(G) will be the set of character degrees of G. We consider groups where no prime divides at least three degrees in cd(G). Benjamin studied this question for solvable groups in [1]. She proved that solvable groups with this property satisfy |cd(G)| 6 6. She also presented examples to show...

Fixed Point Spaces, Primitive Character Degrees and Conjugacy Class Sizes

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

On Finite Groups With Two Irreducible Character Degrees