Compact coGalois groups

In this paper we extend the concept of the group of covering automorphisms associated to a universal covering space phi: U --> X (where X is a connect ed topological manifold), to the case of left (or right) minimal approximat ions. In the case of torsion-free coverings of abelian groups we exhibit a topology on these groups which makes them into topological groups and we gi ve necessary and sufficient conditions for these groups to be compact. Fina lly we prove that when these groups are compact they are pronilpotent (Theo rem 5.3). We also characterize when these groups are torsion-free (Proposit ion 5.4).