Let $G \curvearrowright X$ be a group action. Then $G \curvearrowright X \times X$ through $g \cdot (x, y) = (g \cdot x, g \cdot y)$. I am interested if this 'diagonal' action and its orbits have a special name.
2026-03-30 09:53:48.1774864428
Does this group action construction have a name?
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If I remember correctly, your guess "diagonal action" is a common name for this kind of group action.