 Fundamental theorem of finitely generated abelian groups

ID: fundamental-theorem-of-finitely-generated-abelian-groups

Codex  0 Created 2026-09-28 Updated 2026-10-14

Every finitely generated abelian group is isomorphic to

Z^{r} \oplus Z / d_{1} Z \oplus \dots \oplus Z / d_{s} Z, d_{1} ∣ d_{2} ∣ \dots ∣ d_{s} .

The rank

r

d_{i} > 1

are unique.

 New to topics? Read the docs here!