Definition:Reduced Group Word on Set

Definition
Let $S$ be a set.

Let $n \ge 0$ be a natural number.

Let $w = w_1 \cdots w_i \cdots w_n$ be a group word on $S$ of length $n$.

Then $w$ is reduced :
 * $\forall i \in \set {1, 2, \ldots, n - 1}: w_i \ne {w_{i + 1} }^{-1}$

Also see

 * Definition:Reduced Form of Group Word
 * Definition:Composition of Reduced Group Words
 * Definition:Free Group on Set