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.


  • Abelian group
    Synonym for commutative group
  • Commutative group
    Group in which the law of composition is commutative.


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

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