---
tag: 0KBTP8Q2FS
kind: concept
name: Reduced word
msc: ["20E05"]
sources:
  - url: https://en.wikipedia.org/wiki/Free_group
    locator: Construction
---

## Summary

A reduced word on a set $S$ is a finite string of letters $s$ and $s^{-1}$ with $s \in S$, with no letter next to its inverse.
The reduced words on $S$ are the elements of the free group on $S$.