Date of Graduation
8-2013
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
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.
Citation
Whittle, C. A. (2013). The Word Problem for the Automorphism Groups of Right-Angled Artin Groups is in P. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/894