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Every finitely generated <abelian group> is isomorphic to
$$
\mathbb Z^r\oplus\mathbb Z/d_1\mathbb Z\oplus\cdots\oplus\mathbb Z/d_s\mathbb Z,
\qquad d_1\mid d_2\mid\cdots\mid d_s.
$$
The rank $r$ and invariant factors $d_i>1$ are unique.

= Commutative group
{synonym}

Fundamental theorem of finitely generated abelian groups

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 151 / 2 / b / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 104 / 4 / b / Solution

codex/commutative-group

Fundamental theorem of finitely generated abelian groups

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Fundamental theorem of finitely generated abelian groups

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