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We also give conditions on the relators of a large-type Coxeter group that are necessary and sufficient for the group to be hyperbolic, and we give a normal form for large-type Coxeter groups that is a regular bicombing, thus establishing that all such groups are biautomatic.","abstract_has_math":false,"creators":["Gies, Paul Josef"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rotman, Joseph J."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:52:44Z","date_published":"2011-05-07T12:52:44Z","updated_at":"2026-07-22T22:25:16Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1995 Gies, Paul Josef"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624351","(UMI)AAI9624351"],"render_values":[{"text":"AAI9624351","href":null,"code":true},{"text":"(UMI)AAI9624351","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/20907","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rotman, Joseph J."]},{"key":"dc:creator","label":"Author","values":["Gies, Paul Josef"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:52:44Z","10000-01-01","1995"]},{"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"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Gies, Paul Josef"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624351","(UMI)AAI9624351","http://hdl.handle.net/2142/20907"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We establish a quadratic time algorithm for the word problem and a cubic time algorithm for the conjugacy problem for Coxeter groups of large type. 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