turkmath.org

I will be presenting my paper of the same title from FCT2013. The word problem for finitely generated groups has been extensively studied; the irreducible word problem is a closely related concept, although little seems to be known about finitely generated groups with a recursively enumerable irreducible word problem. After giving a brief introduction of the terminology and geometric intuition behind some of the definitions and previous results, I will present the main result of the paper, which is that for finitely generated groups, having a recursively enumerable irreducible word problem with respect to every finite generating set is equivalent to having a recursive word problem. Time permitting, I will also show that there are groups for which recursive enumerability of the irreducible word problem does depend on the choice of finite generating set, and explore the relationship with the number of ends of a group.