---
tag: 08ABT85339
kind: concept
name: Cyclic subgroup generated by an element
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Cyclic_group
    locator: Definition and notation
---

## Summary

The cyclic subgroup generated by an element of a group is the set of all integer powers of the element.
It is the smallest subgroup that contains the element.