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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. Curtis, Robert Turner Colleges (2008 onwards) > College of Engineering & Physical Sciences School of Mathematics group theory, finite group, simple group, symmetric generation QA Mathematics University of Birmingham 278
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