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## A finite group of composite order n having a subgroup of every order dividing n is not simple

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.14 Solution: Let $p$ be the smallest prime dividing $n$, and write $n = pm$. Now $G$…

## Every abelian simple group has prime order

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.4 Exercise 3.4.1 Solution: Let $G$ be an abelian simple group. Suppose $G$ is infinite. If $x \in G$…