# Tagged: Cayley Table

## A finite group is abelian if and only if its Cayley table is a symmetric matrix

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.10 Prove that a finite group is abelian if and only if its group table is a symmetric matrix. Solution: If...

## Write out the Cayley table for Sym(3), Dih(8), and the quaternion group

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.5 Exercise 1.5.2 Write out the group tables for $S_3$, $D_8$, and $Q_8$. Solution: Group table for $S_3$: 1 (1 2) (1...