[[Group action]]
# Regular group action

A group $G$ is said to act **regularly** or **sharply transitively** on $M$ if the action is both [[free group action|free]] and [[Transitive group action|transitive]], #m/def/group 
i.e. all point stabilizers are $\{ e \}$ and each orbit $Gm = M$ covers the whole space. 
Equivalently, there exists exactly one $g \in G$ such that $gm = m'$ for all $m, m' \in M$.

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#state/tidy | #lang/en | #SemBr