# Group

## Group

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:

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