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## 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…

## Power maps are abelian group homomorphisms

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.22 Let $A$ be an abelian group and fix some $k \in \mathbb{Z}$. Prove that the map…

## The square map is a group homomorphism precisely on abelian groups

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.18 Let $G$ be a group. Show that the map $\varphi : G \rightarrow G$ given by…