---
tag: 0JGEQXQ4AC
kind: concept
name: Presentation of a group
msc: [20F05]
sources:
  - url: https://en.wikipedia.org/wiki/Presentation_of_a_group
    locator: lead section
same_as:
  wikidata: Q915906
  wikipedia: Presentation of a group
---

## Summary

A presentation $\langle S \mid R \rangle$ describes a group by a set $S$ of generators and a set $R$ of relations.
The group is the quotient of the free group on $S$ by the normal subgroup generated by $R$.