Let K be a compact metrizable group and Γ be a group of automorphisms of K. We first show that each α ∈ Γ is distal on K implies Γ itself is distal on K, a local to global correspondence provided Γ is a generalized \bar{FC}-group or K is a connected finite-dimensional group. We also prove a connection between distality and ergodicity which is used to show that ergodic actions of nilpotent groups on compact connected finite-dimensional abelian groups contains ergodic automorphisms.

Partially supported by NSERC postdoctoral fellowship