Scope of Study: My dissertation explores conjugacy in groups that are near to be abelian.  The study requires applications of such classical combinatorial group theory results as Britton's Lemma and Collins' Lemma.  In Addition, a study of powers of rational matrices and their associated polynomial is needed.

Findings and Conclusions:  Algorithms are developed for making decisions about complex zeros of rational polynomials and estimates of the sizes of entries in powers of rational matrices.  These algorithms are carefully put together to yield the main result of the thesis.
Theorem:  The conjugacy problem is solved for HNN extensions of finitely generated abelian groups.