# Tagged: Quaternion Group

## Every quotient of an abelian group is abelian

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.3 Let $A$ be an abelian group and let $B \leq A$. Prove that $A/B$ is abelian. Give an example of...

## Compute the centralizers of each element in Sym(3), Dih(8), and the quaternion group

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.2 Exercise 2.2.4 For each of the groups $S_3$, $D_8$, and $Q_8$, compute the centralizer of each element and find the center of...