{"id":{"repo_id":"birmingham","oai_identifier":"oai:etheses.bham.ac.uk:290"},"canonical_url":"https://search.dev.ndltd.org/etd/birmingham/oai:etheses.bham.ac.uk:290","repository":{"repo_id":"birmingham","name":"University of Birmingham","base_url":"https://etheses.bham.ac.uk/cgi/oai2"},"display":{"title":"Rank 3 permuation characters and maximal subgroups","abstract":"Let G be a transitive permutation group acting on a finite set E. Let P be a stabilizer in G of a point in E. We say G is primitive rank 3 on E if P is maximal in G and P has exactly three orbits on E. For any subgroup H of G, we denote by 1 \\(\\frac{G}{H}\\) the permutation character or permutation module over the complex number field of G on the cosets G/H. Let H and K be subgroups of G. We say 1 \\(\\frac{G}{H}\\) \\(\\leq\\) 1\\(\\frac{G}{K}\\)if 1 \\(\\frac{G}{K}\\) \\(\\leq\\) -1\\(\\frac{G}{H}\\)is either 0 or a character of G. Also a finite group G is called nearly simple primitive rank 3 on E if there exists a quasi-simple group L such that L/Z(L) \\(\\triangleleft\\) G/Z(L) \\(\\leq\\) Aut(L/Z(L)) and G acts as a primitive rank 3 permutation group on some cosets of a subgroup of L. In this thesis we classify all maximal subgroups M of a class of nearly simple primitive rank 3 groups G acting on E such that 1 \\(\\frac{G}{H}\\) \\(\\leq\\) 1 \\(\\frac{G}{H}\\) where P is a stabilizer of a point in E. This result has an application to the study of minimal genus of algebraic curves which admit group actions.","abstract_html":"Let G be a transitive permutation group acting on a finite set E. Let P be a stabilizer in G of a point in E. We say G is primitive rank 3 on E if P is maximal in G and P has exactly three orbits on E. For any subgroup H of G, we denote by 1 \\(\\frac{G}{H}\\) the permutation character or permutation module over the complex number field of G on the cosets G/H. Let H and K be subgroups of G. We say 1 \\(\\frac{G}{H}\\) \\(\\leq\\) 1\\(\\frac{G}{K}\\)if 1 \\(\\frac{G}{K}\\) \\(\\leq\\) -1\\(\\frac{G}{H}\\)is either 0 or a character of G. Also a finite group G is called nearly simple primitive rank 3 on E if there exists a quasi-simple group L such that L/Z(L) \\(\\triangleleft\\) G/Z(L) \\(\\leq\\) Aut(L/Z(L)) and G acts as a primitive rank 3 permutation group on some cosets of a subgroup of L. In this thesis we classify all maximal subgroups M of a class of nearly simple primitive rank 3 groups G acting on E such that 1 \\(\\frac{G}{H}\\) \\(\\leq\\) 1 \\(\\frac{G}{H}\\) where P is a stabilizer of a point in E. This result has an application to the study of minimal genus of algebraic curves which admit group actions.","abstract_has_math":true,"creators":["Tong Viet, Hung Phi"],"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","date_published":"2009","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":["na"]},{"key":"dc:creator","label":"Author","values":["Tong Viet, Hung Phi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2009"]},{"key":"dc:date.issued","label":"Date","values":["2009"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Mathematics & Statistics","Pure 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/290/"]},{"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/290/1/hung_P_PhD09.pdf","http://etheses.bham.ac.uk//id/eprint/290/2/decl_IS_Hung_09_PhD.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let G be a transitive permutation group acting on a finite set E. Let P be a stabilizer in G of a point in E. We say G is primitive rank 3 on E if P is maximal in G and P has exactly three orbits on E. For any subgroup H of G, we denote by 1 \\(\\frac{G}{H}\\) the permutation character or permutation module over the complex number field of G on the cosets G/H. Let H and K be subgroups of G. We say 1 \\(\\frac{G}{H}\\) \\(\\leq\\) 1\\(\\frac{G}{K}\\)if 1 \\(\\frac{G}{K}\\) \\(\\leq\\) -1\\(\\frac{G}{H}\\)is either 0 or a character of G. Also a finite group G is called nearly simple primitive rank 3 on E if there exists a quasi-simple group L such that L/Z(L) \\(\\triangleleft\\) G/Z(L) \\(\\leq\\) Aut(L/Z(L)) and G acts as a primitive rank 3 permutation group on some cosets of a subgroup of L. In this thesis we classify all maximal subgroups M of a class of nearly simple primitive rank 3 groups G acting on E such that 1 \\(\\frac{G}{H}\\) \\(\\leq\\) 1 \\(\\frac{G}{H}\\) where P is a stabilizer of a point in E. This result has an application to the study of minimal genus of algebraic curves which admit group actions."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Rank 3 permuation characters and maximal subgroups"]}]}],"canonical_facts":{"dc:contributor.sponsor":["na"],"dc:creator":["Tong Viet, Hung Phi"],"dc:date":["2009"],"dc:date.issued":["2009"],"dc:description.abstract":["Let G be a transitive permutation group acting on a finite set E. Let P be a stabilizer in G of a point in E. We say G is primitive rank 3 on E if P is maximal in G and P has exactly three orbits on E. For any subgroup H of G, we denote by 1 \\(\\frac{G}{H}\\) the permutation character or permutation module over the complex number field of G on the cosets G/H. Let H and K be subgroups of G. We say 1 \\(\\frac{G}{H}\\) \\(\\leq\\) 1\\(\\frac{G}{K}\\)if 1 \\(\\frac{G}{K}\\) \\(\\leq\\) -1\\(\\frac{G}{H}\\)is either 0 or a character of G. Also a finite group G is called nearly simple primitive rank 3 on E if there exists a quasi-simple group L such that L/Z(L) \\(\\triangleleft\\) G/Z(L) \\(\\leq\\) Aut(L/Z(L)) and G acts as a primitive rank 3 permutation group on some cosets of a subgroup of L. In this thesis we classify all maximal subgroups M of a class of nearly simple primitive rank 3 groups G acting on E such that 1 \\(\\frac{G}{H}\\) \\(\\leq\\) 1 \\(\\frac{G}{H}\\) where P is a stabilizer of a point in E. This result has an application to the study of minimal genus of algebraic curves which admit group actions."],"dc:format":["application/pdf"],"dc:identifier.uri":["http://etheses.bham.ac.uk//id/eprint/290/1/hung_P_PhD09.pdf","http://etheses.bham.ac.uk//id/eprint/290/2/decl_IS_Hung_09_PhD.pdf"],"dc:publisher.department":["School of Mathematics & Statistics","Pure Mathematics"],"dc:publisher.institution":["University of Birmingham"],"dc:relation.isreferencedby":["http://etheses.bham.ac.uk//id/eprint/290/"],"dc:subject":["QA Mathematics"],"dc:title":["Rank 3 permuation characters and maximal subgroups"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["d_ph"],"dc:type.qualificationname":["d_ph"]},"updated_at":"2026-07-24T01:10:50Z"}