{"id":{"repo_id":"birmingham","oai_identifier":"oai:etheses.bham.ac.uk:70"},"canonical_url":"https://search.dev.ndltd.org/etd/birmingham/oai:etheses.bham.ac.uk:70","repository":{"repo_id":"birmingham","name":"University of Birmingham","base_url":"https://etheses.bham.ac.uk/cgi/oai2"},"display":{"title":"Saturated fusion systems and finite groups","abstract":"This thesis is primarily concerned with saturated fusion systems over groups of shape q\\(^r\\) : q where q = p\\(^n\\) for some odd prime p and some natural number n. We shall present two results related to these fusion systems. Our first result is a complete classification of saturated fusion systems over a Sylow p-subgroup of SL\\(_3\\)(q) (which has shape q\\(^3\\) : q). This extends a result of Albert Ruiz and Antonio Viruel, who studied the case when q = p in [36]. As an immediate consequence of this result we shall have a complete classification of p-local finite groups over Sylow p-subgroups of SL\\(_3\\)(q). In the second half of this thesis we shall construct an infinite family of exotic fusion systems over some groups of shape p\\(^r\\) : p. This extends some work of Broto, Levi and Oliver, who studied the case when r = 3 in [12].","abstract_html":"This thesis is primarily concerned with saturated fusion systems over groups of shape q<span class=\"etd-inline-math\"><sup>r</sup></span> : q where q = p<span class=\"etd-inline-math\"><sup>n</sup></span> for some odd prime p and some natural number n. We shall present two results related to these fusion systems. Our first result is a complete classification of saturated fusion systems over a Sylow p-subgroup of SL<span class=\"etd-inline-math\"><sub>3</sub></span>(q) (which has shape q<span class=\"etd-inline-math\"><sup>3</sup></span> : q). This extends a result of Albert Ruiz and Antonio Viruel, who studied the case when q = p in [36]. As an immediate consequence of this result we shall have a complete classification of p-local finite groups over Sylow p-subgroups of SL<span class=\"etd-inline-math\"><sub>3</sub></span>(q). In the second half of this thesis we shall construct an infinite family of exotic fusion systems over some groups of shape p<span class=\"etd-inline-math\"><sup>r</sup></span> : p. This extends some work of Broto, Levi and Oliver, who studied the case when r = 3 in [12].","abstract_has_math":true,"creators":["Clelland, Murray Robinson"],"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":2007,"date_issued":"2007-07","date_published":"2007-07","updated_at":"2026-07-24T01:10:41Z","subjects":["QA Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://etheses.bham.ac.uk//id/eprint/70/2/Decl_IS_Clelland07PhD.jpg","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.sponsor","label":"Sponsor","values":["na"]},{"key":"dc:creator","label":"Author","values":["Clelland, Murray Robinson"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2007-07"]},{"key":"dc:date.issued","label":"Date","values":["2007-07"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Mathematics & Statistics","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/70/"]},{"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/70/1/Clelland07PhD.pdf","http://etheses.bham.ac.uk//id/eprint/70/2/Decl_IS_Clelland07PhD.jpg"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis is primarily concerned with saturated fusion systems over groups of shape q\\(^r\\) : q where q = p\\(^n\\) for some odd prime p and some natural number n. We shall present two results related to these fusion systems. Our first result is a complete classification of saturated fusion systems over a Sylow p-subgroup of SL\\(_3\\)(q) (which has shape q\\(^3\\) : q). This extends a result of Albert Ruiz and Antonio Viruel, who studied the case when q = p in [36]. As an immediate consequence of this result we shall have a complete classification of p-local finite groups over Sylow p-subgroups of SL\\(_3\\)(q). In the second half of this thesis we shall construct an infinite family of exotic fusion systems over some groups of shape p\\(^r\\) : p. This extends some work of Broto, Levi and Oliver, who studied the case when r = 3 in [12]."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf","image/jpeg"]},{"key":"dc:title","label":"Title","values":["Saturated fusion systems and finite groups"]}]}],"canonical_facts":{"dc:contributor.sponsor":["na"],"dc:creator":["Clelland, Murray Robinson"],"dc:date":["2007-07"],"dc:date.issued":["2007-07"],"dc:description.abstract":["This thesis is primarily concerned with saturated fusion systems over groups of shape q\\(^r\\) : q where q = p\\(^n\\) for some odd prime p and some natural number n. We shall present two results related to these fusion systems. Our first result is a complete classification of saturated fusion systems over a Sylow p-subgroup of SL\\(_3\\)(q) (which has shape q\\(^3\\) : q). This extends a result of Albert Ruiz and Antonio Viruel, who studied the case when q = p in [36]. As an immediate consequence of this result we shall have a complete classification of p-local finite groups over Sylow p-subgroups of SL\\(_3\\)(q). In the second half of this thesis we shall construct an infinite family of exotic fusion systems over some groups of shape p\\(^r\\) : p. This extends some work of Broto, Levi and Oliver, who studied the case when r = 3 in [12]."],"dc:format":["application/pdf","image/jpeg"],"dc:identifier.uri":["http://etheses.bham.ac.uk//id/eprint/70/1/Clelland07PhD.pdf","http://etheses.bham.ac.uk//id/eprint/70/2/Decl_IS_Clelland07PhD.jpg"],"dc:publisher.department":["School of Mathematics & Statistics","School of Mathematics"],"dc:publisher.institution":["University of Birmingham"],"dc:relation.isreferencedby":["http://etheses.bham.ac.uk//id/eprint/70/"],"dc:subject":["QA Mathematics"],"dc:title":["Saturated fusion systems and finite groups"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["d_ph"],"dc:type.qualificationname":["d_ph"]},"updated_at":"2026-07-24T01:10:41Z"}