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## The set of all endomorphisms of an abelian group is a ring under pointwise addition and composition

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.29 Let $A$ be any abelian group. Let $R = \mathsf{Hom}(A,A)$ be the set of all group…

## The set of all group automorphisms of a fixed group is a group

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.20 Let $G$ be a group and let $\mathsf{Aut}(G)$ be the set of all isomorphisms \$G \rightarrow…