In abstract algebra, an abelian group is called finitely generated if there exist finitely many elements in such that every in can be written in the form for some integers . In this case, we say that the set is a generating set of or that generate . So, finitely generated abelian groups can be thought of as a generalization of cyclic groups.
Every finite abelian group is finitely generated. The finitely generated abelian groups can be completely classified.
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