Name given to an algebraic structure (G, ⊕) formed by a set G in which we defined an operation noted here as ⊕ responding to the following conditions:

- G has an identity element
*n*for the operation ⊕; - each element
*x*of G has a symmetric*x*‘ in G such as*x*⊕*x*‘ =*n*.

### Properties

**Abelian group**

Synonym for**commutative group**

**Commutative group**Group in which the law of composition is commutative.

### Example

The structure \(\left(\mathbb{Z},+\right)\) is a group in which the identity element is 0.