[[Group action]]
# Transitive group action

A group action $\varphi : G \times M \to M$ is said to be **transitive** iff for every $m, m' \in M$ there exists $g \in G$ such that $\varphi(g,m) = m'$. #m/def/group 
Equivalent statements include

- the [[Group action orbit|orbit]] $Gm$ of any point $m$ is the entire space $M$
- each element acts surjectively on $M$

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