About: Word (group theory)

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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.

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  • 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. (en)
  • 在群論中，字是群的任何元素和它們的逆元寫成的乘積。例如，如果 x, y 和 z 是群 G 的元素，則 xy, z-1xzz 和 y-1zxx-1yz-1 都是集合 {x, y, z} 形成的字。字在自由群和展示理論中扮演重要角色，并是的中心研究對象。 (zh)
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  • 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. (en)
  • 在群論中，字是群的任何元素和它們的逆元寫成的乘積。例如，如果 x, y 和 z 是群 G 的元素，則 xy, z-1xzz 和 y-1zxx-1yz-1 都是集合 {x, y, z} 形成的字。字在自由群和展示理論中扮演重要角色，并是的中心研究對象。 (zh)
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  • Word (group theory) (en)
  • 字 (群論) (zh)
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