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.