In mathematics, a principal homogeneous space, or torsor, for a group G's a homogeneous space X for G such that the stabilizer subgroup of any point's trivial. Equivalently, a principal homogeneous space for a group G's a set X on which G acts freely and transitively, so that for any x, y in X there exists a unique g in G such that x·g = y where · denotes the (right) action of G on X.An analogous definition holds in other categories where, for example, G's a topological group, X's a to… (More on Torsor)