Torsion-free abelian group

In mathematics, specifically in abstract algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is commutative and the identity element is the only element with finite order. That is, multiples of any element other than the identity element generate an infinite number of distinct elements of the group.

An abelian group ${\displaystyle \langle G,*\rangle }$ is a set G, together with a binary operation * on G, such that the following axioms are satisfied:

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