Group Theory

This project involves a question in group theory. In a recent ground-breaking paper by Louder and Touikan (Strong accessibility for finitely presented groups, published May 2017) it was shown that relatively hyperbolic groups with no 2-torsion are strongly accessible. The goal of the project is to show that the same is also true for relatively hyperbolic groups which do have 2-torsion. I have already devised a preliminary modified version of the constructions used in the aforementioned paper for relatively hyperbolic groups with 2-torsion and hopes to show that these modifications (or some other similar ones) allow the result to follow through, initially for nonrelative hyperbolic groups before moving on to the relative case.