Definition:Group of Reduced Group Words

Definition
Let $X$ be a set.

The group of reduced group words on $X$ is the group $(F_X, \cdot)$ where:
 * $F_X$ is the set of reduced group words on $X$.
 * $\cdot$ denotes composition of reduced group words

Also see

 * Group of Reduced Group Words is Group
 * Definition:Free Group on Set