Groups, subgroups, cyclic and permutation groups

By the end you’ll be able to

• Verify group axioms and work with standard groups: $\mathbb{Z}_n$, the unit groups $U(n)$, symmetric groups $S_n$, dihedral groups, matrix groups and the quaternion group
• Find orders of elements and apply Lagrange’s theorem, cosets and index
• Analyse cyclic groups: generators, the unique subgroup of each order dividing $n$ and the Euler phi function