Word (Group Theory)
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High Quality Content by WIKIPEDIA articles! 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. Let G be a group, and let S be a subset of G. A word in S is any expression of the form s_1^{epsilon_1} s_2^{epsilon_2} cdots s_n^{epsilon_n} where s1,...,sn are elements of S and each i is ±1. The number n is…mehr

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High Quality Content by WIKIPEDIA articles! 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. Let G be a group, and let S be a subset of G. A word in S is any expression of the form s_1^{epsilon_1} s_2^{epsilon_2} cdots s_n^{epsilon_n} where s1,...,sn are elements of S and each i is ±1. The number n is known as the length of the word. Each word in S represents an element of G, namely the product of the expression. By convention, the identity element can be represented by the empty word, which is the unique word of length zero.