---
tag: 0RP7VWQ0YN
kind: concept
name: Subgroup generated by a subset
msc: [20A05]
sources:
  - url: https://en.wikipedia.org/wiki/Generating_set_of_a_group
    locator: lead section
---

## Summary

The subgroup generated by a subset of a group is the smallest subgroup that contains the subset.
Its elements are the finite products of elements of the subset and their inverses.