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## Basic properties of the direct sum of groups

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.17 Solution: (1) Note that $\prod 1 \in H$, where we may take $J = \emptyset$. Thus…

## Compute a torsion subgroup

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.7 Fix $n \in \mathbb{Z}^+$ with $n > 1$. Find the torsion subgroup of $\mathbb{Z} \times \mathbb{Z}/(n)$.…

## Torsion elements in an abelian group form a subgroup

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.6 Let $G$ be a group. An element $x \in G$ is called torsion if it has…