Mixed Groups with Decomposition Bases and Global k-Groups

Abstract

This thesis is devoted to proving assertions made without proof by Paul Hill and Charles Megibben in their fundamental papers regarding knice subgroups and the Axiom 3 characterization of global Warfield groups. The main theme throughout is the relationship between the notions of a global k-group and a group with a decomposition basis. Most of our results involve properties of the auxiliary notions of primitive element and *-valuated coproduct in both the mixed and torsion free settings.