We provide an algorithm which takes any given automorphism f of any given right-angled Artin group G and determines whether or not f is the identity automorphism, thereby solving the word problem for the automorphism groups of right-angled Artin groups. We do this by solving the compressed word problem for right-angled Artin groups, a more general result. A key piece of this solution is the use of Plandowski's algorithm. We also demonstrate that our algorithm runs in polynomial time in the size of the given automorphism, written as a word in Laurence's generators of the automorphism group of the given right-angled Artin group.
","abstract_html":"<p>We provide an algorithm which takes any given automorphism <em>f</em> of any given right-angled Artin group <em>G</em> and determines whether or not <em>f</em> is the identity automorphism, thereby solving the word problem for the automorphism groups of right-angled Artin groups. We do this by solving the compressed word problem for right-angled Artin groups, a more general result. A key piece of this solution is the use of Plandowski's algorithm. We also demonstrate that our algorithm runs in polynomial time in the size of the given automorphism, written as a word in Laurence's generators of the automorphism group of the given right-angled Artin group.</p>","abstract_has_math":false,"creators":["Whittle, Carrie Anne"],"institution":null,"degree_name":"Doctor of Philosophy in Mathematics (PhD)","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Goodman-Strauss, Chaim","Arnold, Mark E."],"advisors":["Rieck, Yo’av"],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-08-01T07:00:00Z","date_published":"2013-08-01T07:00:00Z","updated_at":"2026-07-24T00:59:24Z","subjects":["Pure sciences","Applied sciences","Automorphism groups","Graph groups","Partially commutative groups","Polynomial time","Right-angled artin groups","Word problems","Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uark.edu/etd/894","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goodman-Strauss, Chaim","Arnold, Mark E."]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Rieck, Yo’av"]},{"key":"dc:creator","label":"Author","values":["Whittle, Carrie Anne"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-09-29T07:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy in Mathematics (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Pure sciences","Applied sciences","Automorphism groups","Graph groups","Partially commutative groups","Polynomial time","Right-angled artin groups","Word problems","Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uark.edu/etd/894"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We provide an algorithm which takes any given automorphism f of any given right-angled Artin group G and determines whether or not f is the identity automorphism, thereby solving the word problem for the automorphism groups of right-angled Artin groups. We do this by solving the compressed word problem for right-angled Artin groups, a more general result. A key piece of this solution is the use of Plandowski's algorithm. We also demonstrate that our algorithm runs in polynomial time in the size of the given automorphism, written as a word in Laurence's generators of the automorphism group of the given right-angled Artin group.
"]},{"key":"dc:title","label":"Title","values":["The Word Problem for the Automorphism Groups of Right-Angled Artin Groups is in P"]}]}],"canonical_facts":{"dc:contributor":["Goodman-Strauss, Chaim","Arnold, Mark E."],"dc:contributor.advisor":["Rieck, Yo’av"],"dc:creator":["Whittle, Carrie Anne"],"dc:date":["2013"],"dc:date.available":["2017-09-29T07:00:00Z"],"dc:description.abstract":["We provide an algorithm which takes any given automorphism f of any given right-angled Artin group G and determines whether or not f is the identity automorphism, thereby solving the word problem for the automorphism groups of right-angled Artin groups. We do this by solving the compressed word problem for right-angled Artin groups, a more general result. A key piece of this solution is the use of Plandowski's algorithm. We also demonstrate that our algorithm runs in polynomial time in the size of the given automorphism, written as a word in Laurence's generators of the automorphism group of the given right-angled Artin group.
"],"dc:identifier":["https://scholarworks.uark.edu/etd/894"],"dc:subject":["Pure sciences","Applied sciences","Automorphism groups","Graph groups","Partially commutative groups","Polynomial time","Right-angled artin groups","Word problems","Applied Mathematics"],"dc:title":["The Word Problem for the Automorphism Groups of Right-Angled Artin Groups is in P"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy in Mathematics (PhD)"]},"updated_at":"2026-07-24T00:59:24Z"}