Bounding group orders by large character degrees: A question of Snyder

Bounding the Number of Character Degrees of a Solvable Group

A difficult problem in the character theory of solvable groups is to show that the number c.d. (G) of irreducible character degrees of a solvable group G is equal to or greater than d.l. (G), the derived length of G. Isaacs [4] has shown that d.l. (G) ^ 3 c.d. (G)-2 for every solvable group. Berger [1] subsequently proved that d.l. (G) < c.d. (G) when | G | is odd. This problem belongs to the c...

Symmetric Group Character Degrees and Hook Numbers

In this article we prove the following result: that for any two natural numbers k and `, and for all sufficiently large symmetric groups Sn, there are k disjoint sets of ` irreducible characters of Sn, such that each set consists of characters with the same degree, and distinct sets have different degrees. In particular, this resolves a conjecture most recently made by Moretó in [5]. The method...

Bounding nonsplitting enumeration degrees

1-Generic Degrees Bounding Minimal Degrees Revisited

We show that over the base system P− + Σ2-bounding, the existence of a 1-generic degree < 0′′ bounding a minimal degree is equivalent to Σ2-induction.

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...