A group action G×X->X is transitive if it possesses only a single group orbit, i.e., for every pair of elements x and y, there is a group element g such that g x = y. In this case, X is isomorphic to the left cosets of the isotropy group, X~G/G_x. The space X, which has a transitive group action, is called a homogeneous space when the group is a Lie group.

effective action | faithful group action | free action | group | group orbit | group representation | isotropy group | Lie group quotient space | matrix group | topological group | transitive group