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Title: On the symmetric generation of finite groups
Author: Fairbairn, Benjamin Thomas
ISNI:       0000 0004 2686 005X
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2009
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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.
Supervisor: Not available Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics