{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86979"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86979","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Chain Conditions for Subgroups of Infinite Order or Index","abstract":"Groups with max-infinityi or min-infinityi for i=empty,s,n are the subject of this dissertation. Abelian, nilpotent, and solvable groups with max-infinity or min-infinity are examined in detail and structure theorems are given in each case. We then characterize the groups with max-infinity or min-infinity in the smallest class of groups containing all linear groups which is locally closed and closed with respect to the formation of ascending series with factors in the class. In addition, we discuss characterizations of solvable groups and subsolvable groups with max-infinitys or min-infinitys. Investigations of locally nilpotent and metanilpotent groups with max-infinityn or min-infinity n are included as final topics.","abstract_html":"Groups with max-infinityi or min-infinityi for i=empty,s,n are the subject of this dissertation. Abelian, nilpotent, and solvable groups with max-infinity or min-infinity are examined in detail and structure theorems are given in each case. We then characterize the groups with max-infinity or min-infinity in the smallest class of groups containing all linear groups which is locally closed and closed with respect to the formation of ascending series with factors in the class. In addition, we discuss characterizations of solvable groups and subsolvable groups with max-infinitys or min-infinitys. Investigations of locally nilpotent and metanilpotent groups with max-infinityn or min-infinity n are included as final topics.","abstract_has_math":false,"creators":["Paek, Dae Hyun"],"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":"2015-09-28T15:20:27Z","date_published":"2015-09-28T15:20:27Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9944958"],"render_values":[{"text":"(MiAaPQ)AAI9944958","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86979","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":["Paek, Dae Hyun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:27Z","10000-01-01","1999"]},{"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/2142/86979","(MiAaPQ)AAI9944958"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Groups with max-infinityi or min-infinityi for i=empty,s,n are the subject of this dissertation. Abelian, nilpotent, and solvable groups with max-infinity or min-infinity are examined in detail and structure theorems are given in each case. We then characterize the groups with max-infinity or min-infinity in the smallest class of groups containing all linear groups which is locally closed and closed with respect to the formation of ascending series with factors in the class. In addition, we discuss characterizations of solvable groups and subsolvable groups with max-infinitys or min-infinitys. Investigations of locally nilpotent and metanilpotent groups with max-infinityn or min-infinity n are included as final topics.","Made available in DSpace on 2015-09-28T15:20:27Z (GMT). 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Abelian, nilpotent, and solvable groups with max-infinity or min-infinity are examined in detail and structure theorems are given in each case. We then characterize the groups with max-infinity or min-infinity in the smallest class of groups containing all linear groups which is locally closed and closed with respect to the formation of ascending series with factors in the class. In addition, we discuss characterizations of solvable groups and subsolvable groups with max-infinitys or min-infinitys. Investigations of locally nilpotent and metanilpotent groups with max-infinityn or min-infinity n are included as final topics.","Made available in DSpace on 2015-09-28T15:20:27Z (GMT). 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