= Solution
The <Fundamental theorem of finitely generated abelian groups> says that every finitely generated <abelian group> is isomorphic to
$$
\boxed{\mathbb Z^r\oplus\mathbb Z/d_1\mathbb Z\oplus\cdots\oplus\mathbb Z/d_s\mathbb Z,\qquad
1<d_1\mid d_2\mid\cdots\mid d_s.}
$$
The <rank of an abelian group> $r$ and the invariant factors $d_j$ are uniquely determined, with the finite summand allowed to be absent. Equivalently, one can decompose the torsion subgroup into cyclic groups of prime-power orders. The infinite cyclic part and torsion part must both be included in the statement.
Back to article page
