# 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*^{−1}*xzz* and *y*^{−1}*zxx*^{−1}*yz*^{−1} are words in the set {*x*, *y*, *z*}. Two different words may evaluate to the same value in *G*,[1] or even in every group.[2] Words play an important role in the theory of free groups and presentations, and are central objects of study in combinatorial group theory.