1.Previous
3.Next

and are central objects of study in combinatorial group theory.

Definitions

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,...,s_n are elements of S, called generators, 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

1.Previous
3.Next