{"id":{"repo_id":"birmingham","oai_identifier":"oai:etheses.bham.ac.uk:113"},"canonical_url":"https://search.dev.ndltd.org/etd/birmingham/oai:etheses.bham.ac.uk:113","repository":{"repo_id":"birmingham","name":"University of Birmingham","base_url":"https://etheses.bham.ac.uk/cgi/oai2"},"display":{"title":"A 3-local characterization of the group of the Thompson sporadic simple group","abstract":"In this thesis we characterize the Thompson sporadic simple group by its 3-local structure. We study a faithful completion, \\(G\\), of an amalgam of type F\\(_3\\) with the property that \\(N_G(Z(L_\\beta)) = G_\\beta\\). We first assume no additional 3-local structure and use a \\(\\kappa\\)-proper hypothesis to establish that the completion \\(G\\) with this property contains a subgroup \\(Y\\) of order 3 such that \\(N_G(Y)\\cong (3 \\times\\) G\\(_2\\)(3)) : 2. Secondly, we assume that \\(G\\) contains such a subgroup \\(Y\\) with \\(N_G(Y)\\cong (3 \\times\\) G\\(_2\\)(3)) : 2 and show that for an involution \\(t \\in G, C_G(t)\\) has shape 2\\(^{1+8}_+\\).Alt(9). We then invoke a theorem of Parrott to show that \\(G \\cong \\) Th.","abstract_html":"In this thesis we characterize the Thompson sporadic simple group by its 3-local structure. We study a faithful completion, \\(G\\), of an amalgam of type F<span class=\"etd-inline-math\"><sub>3</sub></span> with the property that <span class=\"etd-inline-math\">N<sub>G</sub>(Z(L<sub>\\</sub>beta)) = G<sub>\\</sub>beta</span>. We first assume no additional 3-local structure and use a \\(\\kappa\\)-proper hypothesis to establish that the completion \\(G\\) with this property contains a subgroup \\(Y\\) of order 3 such that <span class=\"etd-inline-math\">N<sub>G</sub>(Y)\\cong (3 \\times</span> G<span class=\"etd-inline-math\"><sub>2</sub></span>(3)) : 2. Secondly, we assume that \\(G\\) contains such a subgroup \\(Y\\) with <span class=\"etd-inline-math\">N<sub>G</sub>(Y)\\cong (3 \\times</span> G<span class=\"etd-inline-math\"><sub>2</sub></span>(3)) : 2 and show that for an involution <span class=\"etd-inline-math\">t \\in G, C<sub>G</sub>(t)</span> has shape 2<span class=\"etd-inline-math\"><sup>1+8</sup><sub>+</sub></span>.Alt(9). We then invoke a theorem of Parrott to show that \\(G \\cong \\) Th.","abstract_has_math":true,"creators":["Fowler, Rachel Ann Abbott"],"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":"2026-07-24T01:10:46Z","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":["Fowler, Rachel Ann Abbott"]}]},{"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/113/"]},{"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/113/1/FowlerRachel07PhD.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we characterize the Thompson sporadic simple group by its 3-local structure. We study a faithful completion, \\(G\\), of an amalgam of type F\\(_3\\) with the property that \\(N_G(Z(L_\\beta)) = G_\\beta\\). We first assume no additional 3-local structure and use a \\(\\kappa\\)-proper hypothesis to establish that the completion \\(G\\) with this property contains a subgroup \\(Y\\) of order 3 such that \\(N_G(Y)\\cong (3 \\times\\) G\\(_2\\)(3)) : 2. Secondly, we assume that \\(G\\) contains such a subgroup \\(Y\\) with \\(N_G(Y)\\cong (3 \\times\\) G\\(_2\\)(3)) : 2 and show that for an involution \\(t \\in G, C_G(t)\\) has shape 2\\(^{1+8}_+\\).Alt(9). We then invoke a theorem of Parrott to show that \\(G \\cong \\) Th."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A 3-local characterization of the group of the Thompson sporadic simple group"]}]}],"canonical_facts":{"dc:contributor.sponsor":["epsrc"],"dc:creator":["Fowler, Rachel Ann Abbott"],"dc:date":["2007-07"],"dc:date.issued":["2007-07"],"dc:description.abstract":["In this thesis we characterize the Thompson sporadic simple group by its 3-local structure. We study a faithful completion, \\(G\\), of an amalgam of type F\\(_3\\) with the property that \\(N_G(Z(L_\\beta)) = G_\\beta\\). We first assume no additional 3-local structure and use a \\(\\kappa\\)-proper hypothesis to establish that the completion \\(G\\) with this property contains a subgroup \\(Y\\) of order 3 such that \\(N_G(Y)\\cong (3 \\times\\) G\\(_2\\)(3)) : 2. Secondly, we assume that \\(G\\) contains such a subgroup \\(Y\\) with \\(N_G(Y)\\cong (3 \\times\\) G\\(_2\\)(3)) : 2 and show that for an involution \\(t \\in G, C_G(t)\\) has shape 2\\(^{1+8}_+\\).Alt(9). We then invoke a theorem of Parrott to show that \\(G \\cong \\) Th."],"dc:format":["application/pdf"],"dc:identifier.uri":["http://etheses.bham.ac.uk//id/eprint/113/1/FowlerRachel07PhD.pdf"],"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/113/"],"dc:subject":["QA Mathematics"],"dc:title":["A 3-local characterization of the group of the Thompson sporadic simple group"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["d_ph"],"dc:type.qualificationname":["d_ph"]},"updated_at":"2026-07-24T01:10:46Z"}