Symmetric Group and Cycle Decomposition

This lecture covers the Symmetric group, which is the group of all permutations of a set of elements. It explains the concept of cycle decomposition, where permutations are represented as a product of disjoint cycles. The Orbit-Stabilizer theorem is introduced, showing the relationship between the size of an orbit and the index of the stabilizer subgroup. The lecture also delves into the properties of cycles, transpositions, and the alternating group within the context of permutation groups.