Definition:Group of Reduced Group Words

Definition
Let $S$ be a set.

The group of reduced group words on $S$ is the group $\struct {F_S, \circ}$ such that:
 * $F_S$ is the set of reduced group words on $S$
 * $\circ$ denotes composition of reduced group words.

Also see

 * Group of Reduced Group Words is Group


 * Definition:Free Group on Set
 * Definition:Kleene Closure