Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.3 Compute the lattice of subgroups of $Q_8$. Solution: Every $\subseteq$-minimal subgroup of $Q_8$ is cyclic; disregarding…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.2 Find the lattice of subgroups of $S_3$. Solution: Every (nontrivial) $\subseteq$-minimal subgroup of $S_3$ is cyclic…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.6 Let $M = \langle u,v \rangle$ be the modular group of order 16 described in Exercise…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.5 Let $QD_{16} = \langle \sigma, \tau \rangle$ be the quasidihedral group of order 16 described in…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.7 Let $Z_{48} = \langle x \rangle$ and use the isomorphism $\mathbb{Z}/(48) \cong Z_{48}$ given by $\overline{1}…
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.6 In $\mathbb{Z}/(48)$, write out all elements of $\langle \overline{a} \rangle$ for every $\overline{a}$. Find all inclusions…