The rank of a finitely generated abelian group is the number of infinite cyclic factors in its invariant-factor decomposition, equivalently .
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The **rank** of an abelian group is a concept that generally refers to the maximum number of linearly independent elements in the group when it is considered as a module over the integers. For finitely generated abelian groups, the rank can be understood in relation to the structure theorem for finitely generated abelian groups.