On the symmetric generation of finite groups

Fairbairn, Benjamin Thomas (2009). On the symmetric generation of finite groups. University of Birmingham. Ph.D.

Preview

Fairbairn09PhD.pdf
PDF
Download (551kB)

Abstract

In this thesis we discuss some uses and applications of the techniques in Symmetric generation. In Chapter 1 we introduce the notions of symmetric generation. In Chapter 2 we discuss symmetric presentations defined by symmetric generating sets that are preserved by a group acting on them transitively but imprimitively. In Chapter 3 our attention turns to Coxeter groups. We show how the Coxeter-Moser presentations traditionally associated with the families of finite Coxeter groups of types A\(_n\), D\(_n\) and E\(_n\) (ie the “simply laced” Coxeter groups) may be interpreted as symmetric presentations and as such may be naturally arrived at by elementary means. In Chapter 4 we classify the irreducible monomial representations of the groups L\(_2\)(q) and use these to define symmetric generating sets of various groups.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):