abstract:In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G such that the stabilizer subgroup of any point is trivial. Equivalently, a principal homogeneous space for a group G is a non-empty set X on which G acts freely and transitively, meaning 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.