On the structure of submodule of finitely generated module over PID

Rui Xiong

Consider $\mathbb{Z}/8\mathbb{Z}\oplus \mathbb{Z}/2\mathbb{Z}$, and the subgroup generated by $(2,1)$, it is a subgroup isomorphic to $\mathbb{Z}/4\mathbb{Z}$. If my theorem holds,…