Group action

Transitive group action

A group action 𝜑 :𝐺 ×𝑀 →𝑀 is said to be transitive iff for every 𝑚,𝑚′ ∈𝑀 there exists 𝑔 ∈𝐺 such that 𝜑(𝑔,𝑚) =𝑚′. #m/def/group Equivalent statements include

• the orbit 𝐺𝑚 of any point 𝑚 is the entire space 𝑀
• each element acts surjectively on 𝑀

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