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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.
