Transitive Group Action -- from Wolfram MathWorld

Transitive Group Action -- from Wolfram MathWorld: "The space , which has a transitive group action, is called a homogeneous space when the group is a Lie group."



(w) Regular (or simply transitive or sharply transitive) if it is both transitive and free; this is equivalent to saying that for every two x, y in X there exists precisely one g in Gsuch that g⋅x = y. In this case, X is called a principal homogeneous space for G or a G-torsor. 

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