Cayley’s theorem says every group is a permutation group. This part makes that concrete: cycle notation, disjoint-cycle decomposition, transpositions, parity, and the alternating group $A_n$.

Sequence

1. Groups of Permutations — symmetric groups, cycle notation, and Cayley’s theorem.
2. Orbits, Cycles, and the Alternating Groups — even and odd permutations, $A_n$.