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)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)