Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.5 Let $G$ be a finite group with $|G| = n > 2$. Prove that $G$ cannot…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.4 Give an explicit example of a group $G$ and an infinite subset $H$ of $G$ which…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.3 Show that the following subsets of $D_8$ are subgroups. (1) $\{ 1, r^2, s, sr^2 \}$…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.2 Show that in each of the following examples, the specified subset is not a subgroup. (1)…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.1 For each of the following, show that the specified subset is a subgroup of the given…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.14 Let $\varphi : G \rightarrow H$ be a group homomorphism. Define the kernel of $\varphi$ to…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.13 Let $G$ and $H$ be groups and let $\varphi : G \rightarrow H$ be a group…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.2 Exercise 1.2.6 Let $G$ be a group, and let $x,y \in G$ be elements of order 2. Prove…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.27 Let $G$ be a group and let $x \in G$. Prove that $A = \{ x^n…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.26 Let $(G, \star)$ be a group. Show that a nonempty subset $H \subseteq G$ which is…