Category:Transitive Group Actions

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This category contains results about Transitive Group Actions.

Let $G$ be a group.

Let $S$ be a set.

Let $*: G \times S \to S$ be a group action.

The group action is transitive if and only if for any $x, y \in S$ there exists $g \in G$ such that $g * x = y$.

That is, if and only if for all $x \in S$:

$\Orb x = S$

where $\Orb x$ denotes the orbit of $x \in S$ under $*$.