{"id":{"repo_id":"birmingham","oai_identifier":"oai:etheses.bham.ac.uk:278"},"canonical_url":"https://search.dev.ndltd.org/etd/birmingham/oai:etheses.bham.ac.uk:278","repository":{"repo_id":"birmingham","name":"University of Birmingham","base_url":"https://etheses.bham.ac.uk/cgi/oai2"},"display":{"title":"On the symmetric generation of finite groups","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.","abstract_html":"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<span class=\"etd-inline-math\"><sub>n</sub></span>, D<span class=\"etd-inline-math\"><sub>n</sub></span> and E<span class=\"etd-inline-math\"><sub>n</sub></span> (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<span class=\"etd-inline-math\"><sub>2</sub></span>(q) and use these to define symmetric generating sets of various groups.","abstract_has_math":true,"creators":["Fairbairn, Benjamin Thomas"],"institution":"University of Birmingham","degree_name":"d_ph","degree_level":"d_ph","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-07","date_published":"2009-07","updated_at":"2026-07-24T01:10:50Z","subjects":["QA Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.sponsor","label":"Sponsor","values":["epsrc"]},{"key":"dc:creator","label":"Author","values":["Fairbairn, Benjamin Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2009-07"]},{"key":"dc:date.issued","label":"Date","values":["2009-07"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["College of Engineering & Physical Sciences","School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Birmingham"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["http://etheses.bham.ac.uk//id/eprint/278/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["d_ph"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["d_ph"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["QA Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://etheses.bham.ac.uk//id/eprint/278/1/Fairbairn09PhD.pdf","http://etheses.bham.ac.uk//id/eprint/278/2/Decl_IS_Fairbairn09PhD.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On the symmetric generation of finite groups"]}]}],"canonical_facts":{"dc:contributor.sponsor":["epsrc"],"dc:creator":["Fairbairn, Benjamin Thomas"],"dc:date":["2009-07"],"dc:date.issued":["2009-07"],"dc:description.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."],"dc:format":["application/pdf"],"dc:identifier.uri":["http://etheses.bham.ac.uk//id/eprint/278/1/Fairbairn09PhD.pdf","http://etheses.bham.ac.uk//id/eprint/278/2/Decl_IS_Fairbairn09PhD.pdf"],"dc:publisher.department":["College of Engineering & Physical Sciences","School of Mathematics"],"dc:publisher.institution":["University of Birmingham"],"dc:relation.isreferencedby":["http://etheses.bham.ac.uk//id/eprint/278/"],"dc:subject":["QA Mathematics"],"dc:title":["On the symmetric generation of finite groups"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["d_ph"],"dc:type.qualificationname":["d_ph"]},"updated_at":"2026-07-24T01:10:50Z"}