1 vote

Existence of a transitive smooth G-action of $G\times G$

Your gut feeling is correct. Assume there is a smooth, transitive action $\theta\colon G \times G^2 \to G^2$. Pick some $p \in G^2$. As $\theta$ is transitive, the orbit map $\theta^{(p)}\colon G \to ...
Ben Steffan's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible