# On the symmetric generation of finite groups

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

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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: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Curtis, Robert TurnerUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: Engineering and Physical Sciences Research Council
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/278

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