Distal criterion of transitive transformation groups

I. U. Bronshtein

Matematičeskie zametki, Tome 5 (1969) no. 1, pp. 77-80.

Résumé

Let $G$ be a topological group, $H$ a closed subgroup of the group $G$, and $G/H$ a homogeneous space of cosets $Hg(g\in G)$. The group $G$ acts naturally on $G/H$, defining a transitive transformation group $(G/H,G,\pi)$, $(Ha,g)\pi=Hag$ ($a\in G$, $g\in G$). Necessary and sufficient conditions for the distalness of the transformation group $(G/H,G,\pi)$ are indicated.