---
tag: 0DBWXQRXQJ
kind: concept
name: Torsion subgroup
msc: [20K10]
sources:
  - url: https://en.wikipedia.org/wiki/Torsion_subgroup
    locator: lead section
same_as:
  wikidata: Q2293759
  wikipedia: Torsion subgroup
---

## Summary

The torsion subgroup of an abelian group is the subgroup of its elements of finite order.
The quotient by the torsion subgroup is torsion-free.