Symmetric Group and Alternating Group

This lecture covers the Symmetric group, cycle notation, multiplication, and conjugation in S_n, the sign of a permutation, and the Alternating group A_n. It explains how any element of S_n is a product of disjoint cycles, uniquely up to the order of factors. The lecture also discusses the kernel of a permutation, the alternating group as a normal subgroup of even permutations, and the cycle decomposition of permutations.