Determine the rank and the elementary divisors of the group $\mathbb{Z} \times 17\mathbb{Z} \times \mathbb{Z}/18\mathbb{Z} \times \mathbb{Z}/12\mathbb{Z}$.
I get how we have to do it for just finite commutative groups of the form $\mathbb{Z}/a\mathbb{Z} \times \mathbb{Z}/b\mathbb{Z}$ with the chinese remainder theorem, but the $\mathbb{Z} \times 17\mathbb{Z}$ throw me off, how does that fit in the picture with factor groups?