On the subgroups of finite Abelian groups of rank three

Mario Hampejs, László Tóth

We describe the subgroups of the group ${\mathbb{Z}}_m\times {\mathbb{Z}}_n\times {\mathbb{Z}}_r$ and derive a simple formula for the total number $s(m,n,r)$ of the subgroups, where $m,n,r$ are arbitrary posi…