This award supports research on linear groups over some classes of division rings and to automorphism groups of free groups and free soluble groups. The principal investigator recently proved that the Tits alternative holds for groups of automorphisms of finitely generated free soluble groups. He will continue this work, as well as study groups of automorphisms of free groups of finite rank. He will also work on extending his result on imbedding a universal enveloping algebra into a division ring to division rings of fractions of torsion free nilpotent groups and the universal fields of fractions of free groups rings. A ring is an algebraic object having both an addition and a multiplication defined on it. These structures arise naturally in many different settings and are of interest in mathematics, computer science, engineering and physics. This particular project blends the study of rings with the study of another algebraic object called a group.
