###### 1.

Determine the order of $(1,2)$ in ${\mathbb Z_4}\times{\mathbb Z_8}\text{.}$

###### 2.

List three properties of a group that are preserved by an isomorphism.

###### 3.

Find a group isomorphic to $\mathbb Z_{15}$ that is an external direct product of two non-trivial groups.

###### 4.

Explain why we can now say “the infinite cyclic group”?

###### 5.

Compare and contrast external direct products and internal direct products.