Linked from

The 16 pages that link to Abelian group, each with the reason it gives.

• Vector spaceBroader topic: The vector-addition axioms require vectors to add commutatively.

• Group theoryBroader topic: This special case has extra structure and simpler classification results.

• GroupBroader topic: Commutativity is an additional property, not a requirement for groups in general.

• Ring (mathematics)Narrower topic: Ring addition must make the elements into an Abelian group.

• Commutative ringRelated: The addition operation in every ring forms an abelian group.

• Homology groupNarrower topic: Homology groups are abelian, so their elements can be added without regard to order.

• Simple groupCompared with: Among nontrivial abelian groups, simplicity occurs exactly at prime order.

• LatticeNarrower topic: Under addition, a lattice is a free Abelian group generated by its basis vectors.

• Chain complexNarrower topic: Chain groups are abelian groups, making sums of chains and their boundaries well-defined.

• Finite simple groupCompared with: Among finite simple groups, only cyclic groups of prime order are abelian.

• Solvable groupRelated: Abelian quotients are the successive simple layers in a solvable group's structure.

• Finite cyclic groupNarrower topic: Every cyclic group is abelian, but many finite abelian groups need multiple generators.

• Commutative propertyBroader topic: This algebraic structure makes commutativity one of its defining requirements.

• Kronecker–Weber theoremRelated: The extension qualifies precisely when its Galois group is abelian.

• Pontryagin dualityNarrower topic: Commutativity is essential to the character-based duality in this form.

• Ring theoryRelated: The additive structure of every ring is an abelian group.