Groups with Two Extreme Character Degrees and their Minimal Faithful Representations

Groups with Two Extreme Character Degrees and Their Normal Subgroups

We study the finite groups G for which the set cd(G) of irreducible complex character degrees consists of the two most extreme possible values, that is, 1 and |G : Z(G)|1/2. We are easily reduced to finite p-groups, for which we derive the following group theoretical characterization: they are the p-groups such that |G : Z(G)| is a square and whose only normal subgroups are those containing G′ ...

On minimal degrees of faithful quasi-permutation representations of nilpotent groups

By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....

On Finite Groups With Two Irreducible Character Degrees

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...

Minimal Faithful Permutation Degrees for Irreducible Coxeter Groups

The minimal faithful degree of a finite group G, denoted by μ(G), is the least non-negative integer n such that G embeds inside Sym(n). In this article we calculate the minimal faithful permutation degree for all of the irreducible Coxeter groups.

On Minimal Faithful Permutation Representations of Finite Groups

The minimal faithful permutation degree n(G) of a finite group G is the least positive integer n such that G is isomorphic to a subgroup of the symmetric group Sn. Let AT be a normal subgroup of a finite group G. We prove that n(G/N) $C /i(G) if G/N has no nontrivial Abelian normal subgroup. There is an as yet unproved conjecture that the same conclusion holds if G/N is Abelian. We investigate ...