Distal actions and ergodic actions on compact groups

Let $K$ be a compact metrizable group and $\text{Ga}$ be a group of automorphisms of $K$. We first show that each $\text{ap}\in \text{Ga}$ is distal on $K$ implies $\text{Ga}$ itself is distal on $K$, a local to global correspondence provided $\text{Ga}$ is a generalized $\text{ov}FC$-group or $K$ is a connected finite-dimensional group. We show that $\text{Ga}$ contains an ergodic automorphism when $\text{Ga}$ is nilpotent and ergodic on a connected finite-dimensional compact abelian group $K$.