Groups with a Character of Large Degree Noah

Groups with a Character of Large Degree

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.

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...

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.

Interpretive study of the request of Prophet Noah (AS) in verse 45 of Hood

The request of Prophet Noah (AS) to God Almighty in verses 45-47 of Surah Hood has long been the subject of controversy among theologians and commentators with various theological tendencies, the interpretive outcome of which has sometimes been in conflict with the status of infallibility. The present article seeks to explain the authorchr('39')s favorite view in an argumentative manner. Howeve...