If $G$ is a group and $N$ is a normal subgroup of $G$, then the operation on the set of left cosets of $N$
\[ (aN)*(bN) = (ab)N\]
is well-defined. The result is a group, called a **quotient group** of $G$ by $N$.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by Jennifer Paulhus on 2022-07-18 16:11:29

**Referred to by:**

- columns.gps_subgroups.quotient
- columns.gps_subgroups.quotient_abelian
- columns.gps_subgroups.quotient_cyclic
- columns.gps_subgroups.quotient_solvable
- group.abelianization
- group.commutator_subgroup
- group.maximal_quotient
- group.nonsplit_product
- group.quotient_isolabel
- group.subgroup.projective_image
- lmfdb/groups/abstract/main.py (line 1241)

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