{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/34463"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/34463","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The Dehn function, word problem, and bounded word problem for finitely generated decidable group presentations","abstract":"For finite group presentations, the word problem is solvable if and only if the Dehn function is computable. Additionally, the bounded word problem is always solvable. For finitely generated decidable group presentations, this is not always the case. The main result of the present work is to determine whether there exist examples of finitely generated decidable group presentations for each combination of solvability/unsolvability of the word problem, solvability/unsolvability of the bounded word problem, and computability/uncomputability of the Dehn function.","abstract_html":"For finite group presentations, the word problem is solvable if and only if the Dehn function is computable. Additionally, the bounded word problem is always solvable. For finitely generated decidable group presentations, this is not always the case. The main result of the present work is to determine whether there exist examples of finitely generated decidable group presentations for each combination of solvability/unsolvability of the word problem, solvability/unsolvability of the bounded word problem, and computability/uncomputability of the Dehn function.","abstract_has_math":false,"creators":["Cummins, Desmond"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ivanov, Sergei V.","Kapovitch, Ilia","Leininger, Christopher J.","Schupp, Paul E."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-09-18T21:18:24Z","date_published":"2012-09-18T21:18:24Z","updated_at":"2026-07-22T22:25:31Z","subjects":["Group Theory","Dehn Function","Word Problem","Bounded Word Problem"],"languages":["en"],"rights":["Copyright 2012 Desmond Cummins"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/34463","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ivanov, Sergei V.","Kapovitch, Ilia","Leininger, Christopher J.","Schupp, Paul E."]},{"key":"dc:creator","label":"Author","values":["Cummins, Desmond"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-09-18T21:18:24Z","2014-09-18T10:01:01Z","2012-08"]},{"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":["Group Theory","Dehn Function","Word Problem","Bounded Word Problem"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 Desmond Cummins"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/34463"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["For finite group presentations, the word problem is solvable if and only if the Dehn function is computable. Additionally, the bounded word problem is always solvable. For finitely generated decidable group presentations, this is not always the case. The main result of the present work is to determine whether there exist examples of finitely generated decidable group presentations for each combination of solvability/unsolvability of the word problem, solvability/unsolvability of the bounded word problem, and computability/uncomputability of the Dehn function.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-11T14:56:02Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Cummins_Desmond.pdf: 741090 bytes, checksum: 806fff69ab6f60e40d6c1f5fa170f03c (MD5)","Made available in DSpace on 2012-09-18T21:18:24Z (GMT). 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Additionally, the bounded word problem is always solvable. For finitely generated decidable group presentations, this is not always the case. The main result of the present work is to determine whether there exist examples of finitely generated decidable group presentations for each combination of solvability/unsolvability of the word problem, solvability/unsolvability of the bounded word problem, and computability/uncomputability of the Dehn function.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-11T14:56:02Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Cummins_Desmond.pdf: 741090 bytes, checksum: 806fff69ab6f60e40d6c1f5fa170f03c (MD5)","Made available in DSpace on 2012-09-18T21:18:24Z (GMT). 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