Linked from

The 23 pages that link to Quotient group, each with the reason it gives.

• Congruence relationBroader topic: It is the group-theoretic quotient produced by a congruence.

• SubgroupCompared with: It compresses a group by a normal subgroup rather than selecting a subgroup within it.

• Abstract algebraBroader topic: Quotients build new structures by collapsing a subgroup while preserving group laws.

• Cyclic groupRelated: Every quotient of a cyclic group is cyclic, since the generator’s coset generates it.

• Universal propertyBroader topic: Its canonical map is universal among homomorphisms that send the normal subgroup to the identity.

• Normal subgroupBroader topic: Normality is the condition that makes coset multiplication well-defined.

• Quotient ringCompared with: It uses the same coset construction, but multiplication requires an ideal rather than merely a subgroup.

• Abelian groupRelated: Quotients of Abelian groups are Abelian, since commutativity passes to cosets.

• CosetRelated: Cosets become quotient-group elements when the subgroup is normal.

• Homology groupRelated: The cycle subgroup is quotiented by its subgroup of boundaries.

• Quotient spaceNarrower topic: The vector-space construction is a special case of quotienting algebraic structures.

• Exact sequenceRelated: In a short exact sequence of groups, the final nonzero map often identifies this quotient.

• Simple groupRelated: Every proper nontrivial normal subgroup would produce a nontrivial quotient.

• CokernelRelated: In groups, the cokernel is the quotient of the codomain by the image subgroup.

• Composition seriesRelated: The simple quotients between consecutive terms are the series' factors.

• Finite simple groupRelated: A finite simple group has no quotient other than itself and the trivial group.

• Jordan–Hölder theoremRelated: Successive quotients determine the factors whose isomorphism types are fixed.

• Equivalence classBroader topic: Its elements are equivalence classes that preserve group structure.

• Quotient setBroader topic: It is a structured quotient set whose group operation is well-defined on classes.

• Isomorphism theoremsBroader topic: Quotients are the structures the theorems compare with subgroups and images.

• Zassenhaus lemmaRelated: Each isomorphic section in the lemma is a quotient of a subgroup.

• Frattini's argumentRelated: The generated-factorization statement can be read as a generation claim modulo the normal subgroup.

• Fundamental theorem on homomorphismsRelated: Quotienting by the kernel creates the theorem's domain-side group.