Rank of an abelian group is analogous to the dimension of a vector space. The main difference with the case of vector space is a presence of torsion. An element of an abelian group "A" is classified as torsion if its order is finite. The set of all torsion elements is a subgroup, called the torsion subgroup and denoted "T"("A"). A group is called torsion-free if it has no non-trivial torsion elements. The factor-group "A"/"T"("A") is the unique maximal torsion-free quotient of "A" and its rank coincides with the rank of "A".