Distal criterion of transitive transformation groups

Let G be a topological group, H a closed subgroup of the group G, and G/H a homogeneous space of cosets Hg(g G). The group G acts naturally on G/H, defining a transitive transformation group (G/H, G,gp), (Ha, g)=Hag(a G, g G). Necessary and sufficient conditions for the distalness of the transformation group (G/H, G,) are indicated.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 77–80, January, 1969.