# Definition:Reduced Group Word on Set

## Definition

Let $S$ be a set.

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

Let $w$ be a group word on $S$ of length $n$.

Then $w$ is reduced if and only if $w_i \neq w_{i+1}^{-1}$ for all $i \in \{1, \ldots, n-1\}$