#### Date of Graduation

8-2013

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy in Mathematics (PhD)

#### Degree Level

Graduate

#### Department

Mathematical Sciences

#### Advisor

Yo'av Rieck

#### Committee Member

Chaim Goodman-Strauss

#### Second Committee Member

Mark E. Arnold

#### Keywords

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

#### 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.

#### Recommended Citation

Whittle, Carrie Anne, "The Word Problem for the Automorphism Groups of Right-Angled Artin Groups is in P" (2013). *Theses and Dissertations*. 894.

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