Word (group theory)

In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z^-1xzz and y^-1zxx^-1yz^-1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, or even in every group. Words play an important role in the theory of free groups and presentations, and are central objects of study in combinatorial group theory.