Groups with a Character of Large Degree

Groups with Two Extreme Character Degrees and their Minimal Faithful Representations

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

Groups with a Character of Large Degree Noah

Let G be a finite group of order n and V a simple C[G]-module of dimension d. For some nonnegative number e, we have n = d(d + e). If e is small, then the character of V has unusually large degree. We fix e and attempt to classify such groups. For e ≤ 3 we give a complete classification. For any other fixed e we show that there are only finitely many examples.

On Finite Groups With Two Irreducible Character Degrees

Finite p-groups with few non-linear irreducible character kernels

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

Solvable groups whose character degree graphs have non-trivial fundamental groups

In this talk, we introduce the character degree graph of a finite group G. We will discuss various properties of this graph, and we will further discuss what graphs can occur as the character degree graphs of finite solvable groups. In particular, we focus on groups with characters of degree pq, pr, and qr, where p, q, and r are distinct primes. Although some group theory will be assumed, knowl...