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,[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.


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