{"id":{"repo_id":"lancaster","oai_identifier":"oai:eprints.lancs.ac.uk:88895"},"canonical_url":"https://search.dev.ndltd.org/etd/lancaster/oai:eprints.lancs.ac.uk:88895","repository":{"repo_id":"lancaster","name":"Lancaster University","base_url":"https://eprints.lancs.ac.uk/cgi/oai2"},"display":{"title":"On extending Scott modules","abstract":"We study a variety of questions related to the Scott modules S(G,Q) associated to a finite group G, where Q denotes a p-subgroup of G for a given prime p. The main concept we study is that of a p-extendible group, which we define to be a group in which the dimension of S(G,Q) is minimal for all p-subgroups Q of G. We study those Frobenius groups which are p-extendible and complete a classification of the local subgroups of the sporadic groups which are p-extendible. Furthermore, we study Scott modules associated to finite classical groups which admit (B,N)-pairs that are split at characteristic p. The thesis concludes with some considerations about the second relative syzygy with respect to a subgroup Q for a certain class of p-groups P.","abstract_html":"We study a variety of questions related to the Scott modules S(G,Q) associated to a finite group G, where Q denotes a p-subgroup of G for a given prime p. The main concept we study is that of a p-extendible group, which we define to be a group in which the dimension of S(G,Q) is minimal for all p-subgroups Q of G. We study those Frobenius groups which are p-extendible and complete a classification of the local subgroups of the sporadic groups which are p-extendible. Furthermore, we study Scott modules associated to finite classical groups which admit (B,N)-pairs that are split at characteristic p. The thesis concludes with some considerations about the second relative syzygy with respect to a subgroup Q for a certain class of p-groups P.","abstract_has_math":false,"creators":["Gullon, Alec","Mazza, Nadia"],"institution":"Lancaster University","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-24T02:48:40Z","subjects":[],"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:creator","label":"Author","values":["Gullon, Alec","Mazza, Nadia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"key":"dc:publisher.commercial","label":"Dc Publisher Commercial","values":["Lancaster University"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Mathematics and Statistics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["Lancaster University"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://eprints.lancs.ac.uk/id/eprint/88895/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://eprints.lancs.ac.uk/id/eprint/88895/1/thesis.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We study a variety of questions related to the Scott modules S(G,Q) associated to a finite group G, where Q denotes a p-subgroup of G for a given prime p. The main concept we study is that of a p-extendible group, which we define to be a group in which the dimension of S(G,Q) is minimal for all p-subgroups Q of G. We study those Frobenius groups which are p-extendible and complete a classification of the local subgroups of the sporadic groups which are p-extendible. Furthermore, we study Scott modules associated to finite classical groups which admit (B,N)-pairs that are split at characteristic p. The thesis concludes with some considerations about the second relative syzygy with respect to a subgroup Q for a certain class of p-groups P."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On extending Scott modules"]}]}],"canonical_facts":{"dc:creator":["Gullon, Alec","Mazza, Nadia"],"dc:date":["2017"],"dc:date.issued":["2017"],"dc:description.abstract":["We study a variety of questions related to the Scott modules S(G,Q) associated to a finite group G, where Q denotes a p-subgroup of G for a given prime p. The main concept we study is that of a p-extendible group, which we define to be a group in which the dimension of S(G,Q) is minimal for all p-subgroups Q of G. We study those Frobenius groups which are p-extendible and complete a classification of the local subgroups of the sporadic groups which are p-extendible. Furthermore, we study Scott modules associated to finite classical groups which admit (B,N)-pairs that are split at characteristic p. The thesis concludes with some considerations about the second relative syzygy with respect to a subgroup Q for a certain class of p-groups P."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://eprints.lancs.ac.uk/id/eprint/88895/1/thesis.pdf"],"dc:publisher.commercial":["Lancaster University"],"dc:publisher.department":["Mathematics and Statistics"],"dc:publisher.institution":["Lancaster University"],"dc:relation.isreferencedby":["https://eprints.lancs.ac.uk/id/eprint/88895/"],"dc:title":["On extending Scott modules"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D."]},"updated_at":"2026-07-24T02:48:40Z"}