Definition
Let G be a group, and let S be a subset of G. A word in S is any expression of the form
where s1,...,sn are elements of S and each εi 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.
Read more about this topic: Word (group Theory)
Famous quotes containing the word definition:
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
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—Adrienne Rich (b. 1929)