Definition:Composition of Reduced Group Words

Definition
Let $X$ be a set.

Let $v$ and $w$ be reduced group words on $X$.

The composition of $v$ and $w$ is the reduced form of their concatenation:
 * $v \cdot w = \operatorname{red}(vw)$

Also see

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