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## Exhibit a group homomorphism from Z/(8) to Z/(4)

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.10 Let $\varphi : \mathbb{Z}/(8) \rightarrow \mathbb{Z}/(4)$ be defined by $\overline{a} \mapsto \overline{a}$. (Note that $\overline{a}$ means…

## On finite groups, power maps with exponent relatively prime to the group order are surjective

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.25 Let $G$ be a cyclic group of order $n$ and let $k$ be an integer relatively…