  One of the most studied algebraic structures with one operation is the
Abelian group, which is defined as a structure whose operation satisfies the
associative and commutative properties, has identical element and every element
has an inverse element. In this article, we characterize the Abelian groups
with other properties and we even reduce it to two the list of properties to be
fulfilled by the operation. For this, we make use of properties that, in
general, are hardly ever mencioned.
