On the Indecomposable Representations of a Certain Class of Groups

On generalized reduced representations of restricted Lie superalgebras in prime characteristic

Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...

Indecomposable Representations and the Loop-space Operation1

For a certain class of algebras, including group-algebras of finite groups, we shall introduce a permutation in the set of isomorphismclasses of nonprojective indecomposable modules. This permutation is in essence given by the loop-space functor [2]. It is to be hoped that the study of this permutation may give some insight into the difficult problem of classifying indecomposable representation...

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...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

Representations of symmetric groups

In this thesis we study the ordinary and the modular representation theory of the symmetric group. In particular we focus our work on different important open questions in the area. 1. Foulkes’ Conjecture In Chapter 2 we focus our attention on the long standing open problem known as Foulkes’ Conjecture. We use methods from character theory of symmetric groups to determine new information on the...