isomorphism of algebra Let $G,K$, and $H$ be a finitely generated commutative group.
If $G\times K$ is isomorphic to $H\times K$, then $G$ is isomorphic to $H$.
Can you guys give me a hint? I don't know how to solve this

It is a consequence of the Fundamental Theorem that every finitely generated commutative group $G$ can be decomposed as a direct product of infinite cyclic group and finite cyclic groups of prime power order, and the orders of these indecomposable factors are uniquely determined by $G$. Your result follows easily from that, but it would be difficult to prove it without using the Fundamental Theorem.
