{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86964"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86964","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Groups in Which Commutativity Is a Transitive Relation","abstract":"A group G is called a CT-group if commutativity is a transitive relation on the set of non-identity elements of G. This dissertation is concerned with the class of CT-groups. Finite and locally finite CT-groups are studied in detail with structure theorems given in both solvable and insolvable cases. The investigation of solvable CT-groups leads naturally to the study of fixed-point-free groups of automorphisms of abelian groups. Topics include a rank condition for the existence of fixed-point-free groups of automorphisms of abelian torsion groups, and the extensions of abelian groups by locally finite groups with fixed-point-free actions. Torsion-free solvable CT-groups and polycyclic CT-groups are also examined in detail with constructions and structure theorems. An additional topic studied is the subclass of groups in which all quotients of subgroups are CT.","abstract_html":"A group G is called a CT-group if commutativity is a transitive relation on the set of non-identity elements of G. This dissertation is concerned with the class of CT-groups. Finite and locally finite CT-groups are studied in detail with structure theorems given in both solvable and insolvable cases. The investigation of solvable CT-groups leads naturally to the study of fixed-point-free groups of automorphisms of abelian groups. Topics include a rank condition for the existence of fixed-point-free groups of automorphisms of abelian torsion groups, and the extensions of abelian groups by locally finite groups with fixed-point-free actions. Torsion-free solvable CT-groups and polycyclic CT-groups are also examined in detail with constructions and structure theorems. An additional topic studied is the subclass of groups in which all quotients of subgroups are CT.","abstract_has_math":false,"creators":["Wu, Yu-Fen"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Derek J.S.Robinson"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:23Z","date_published":"2015-09-28T15:20:23Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9904628"],"render_values":[{"text":"(MiAaPQ)AAI9904628","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86964","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Derek J.S.Robinson"]},{"key":"dc:creator","label":"Author","values":["Wu, Yu-Fen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:23Z","10000-01-01","1998"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86964","(MiAaPQ)AAI9904628"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A group G is called a CT-group if commutativity is a transitive relation on the set of non-identity elements of G. This dissertation is concerned with the class of CT-groups. Finite and locally finite CT-groups are studied in detail with structure theorems given in both solvable and insolvable cases. The investigation of solvable CT-groups leads naturally to the study of fixed-point-free groups of automorphisms of abelian groups. Topics include a rank condition for the existence of fixed-point-free groups of automorphisms of abelian torsion groups, and the extensions of abelian groups by locally finite groups with fixed-point-free actions. Torsion-free solvable CT-groups and polycyclic CT-groups are also examined in detail with constructions and structure theorems. An additional topic studied is the subclass of groups in which all quotients of subgroups are CT.","Made available in DSpace on 2015-09-28T15:20:23Z (GMT). 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Finite and locally finite CT-groups are studied in detail with structure theorems given in both solvable and insolvable cases. The investigation of solvable CT-groups leads naturally to the study of fixed-point-free groups of automorphisms of abelian groups. Topics include a rank condition for the existence of fixed-point-free groups of automorphisms of abelian torsion groups, and the extensions of abelian groups by locally finite groups with fixed-point-free actions. Torsion-free solvable CT-groups and polycyclic CT-groups are also examined in detail with constructions and structure theorems. An additional topic studied is the subclass of groups in which all quotients of subgroups are CT.","Made available in DSpace on 2015-09-28T15:20:23Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9904628.pdf: 2619459 bytes, checksum: 1506137bd26a4da6cf9441746c3dc3b1 (MD5) Previous issue date: 1998","Embargo set by: Seth Robbins for item 88245 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","64 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998."],"dc:identifier":["http://hdl.handle.net/2142/86964","(MiAaPQ)AAI9904628"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Groups in Which Commutativity Is a Transitive Relation"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}