The group F_S on a set S consists of reduced words in S and S^{-1}; it satisfies the universal property that any function S → G (group) extends uniquely to a homomorphism F_S → G.
The group F_S on a set S consists of reduced words in S and S^{-1}; it satisfies the universal property that any function S → G (group) extends uniquely to a homomorphism F_S → G.