##  [Abelian Group](/index.php/abelian-group) 

  ##  [Abelian Group](https://mathlogic.quantumdictionary.io/abelian-group-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/index.php/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A group whose binary operation is commutative for every pair of elements; that is, for all a and b in the group, a * b = b * a.

 

 

 

 

 





 

 



 ##  [Abelian Group](https://puremath.quantumdictionary.io/abelian-group-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A group whose binary operation is commutative, so that for all elements a and b one has a·b = b·a.

 

 

 

 

 





 

 



 ##  [Abelian Group](https://algebra.quantumdictionary.io/abelian-group-2) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A group (G, ·) whose binary operation is commutative: for all a, b in G, a·b = b·a. Equivalently, a group in which every pair of elements commutes under the group law.