The Word Problem for the Automorphism Groups of Right-Angled Artin Groups is in P

<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>

Name thesis:degree_name

Doctor of Philosophy in Mathematics (PhD)

Level thesis:degree_level

Dissertation

Year dc:date.available

2013

Author dc:creator

• Whittle, Carrie Anne

Advisor dc:contributor.advisor

• Rieck, Yo’av

Contributors dc:contributor

• Goodman-Strauss, Chaim
• Arnold, Mark E.

• Pure sciences
• Applied sciences
• Automorphism groups
• Graph groups
• Partially commutative groups
• Polynomial time
• Right-angled artin groups
• Word problems
• Applied Mathematics

Repository record dc:identifier

https://scholarworks.uark.edu/etd/894

OAI identifier oai:identifier

oai:scholarworks.uark.edu:etd-1893