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}. Words play an important role in the theory of free groups and presentations, and are central objects of study in combinatorial group theory.
Read more about Word (group Theory): Definition, Notation, Words and Presentations, Reduced Words, Normal Forms, Operations On Words, The Word Problem
Famous quotes containing the word word:
“If there is anything so romantic as that castle-palace-fortress of Monaco I have not seen it. If there is anything more delicious than the lovely terraces and villas of Monte Carlo I do not wish to see them. There is nothing beyond the semi-tropical vegetation, the projecting promontories into the Mediterranean, the all-embracing sweep of the ocean, the olive groves, and the enchanting climate! One gets tired of the word beautiful.”
—M. E. W. Sherwood (1826–1903)