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Reading Questions 9.3 Reading Questions

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.