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 $w_i \ne w_{i + 1}^{-1}$ for all $i \in \set {1, \ldots, n - 1}$

Also see

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

Examples

 * Empty Group Word is Reduced