If $G$ is a group, a subset $H\subseteq G$ is a **subgroup** of $G$ if the binary operation of $G$ restricts to a binary operation on $H$, and $H$ is a group for this induced operation.

Equivalently, the subset $H$ must satisfy the following conditions:

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2018-08-06 04:03:10

**Referred to by:**

- gg.resolvents
- group.alternating
- group.central
- group.characteristic_subgroup
- group.commutator_subgroup
- group.core
- group.coset
- group.fitting_subgroup
- group.inner_automorphism
- group.lower_central_series
- group.normal_series
- group.radical
- group.semidirect_product
- group.socle
- group.subgroup.centralizer
- group.subgroup.hall
- group.subgroup.normal
- group.subgroup.normal_closure
- group.subgroup.normalizer
- group.sylow_subgroup
- rcs.cande.gg
- ring.ideal

**History:**(expand/hide all)

- 2018-08-06 04:03:10 by John Jones (Reviewed)