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On the symmetric generation of finite groups

Fairbairn, Benjamin Thomas (2009)
Ph.D. thesis, University of Birmingham.

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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:Ph.D. thesis.
Supervisor(s):Curtis, Robert Turner
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Keywords:group theory, finite group, simple group, symmetric generation
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:278
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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