Permutations and Adjacency

This lecture discusses the concept of permutations preserving adjacency, focusing on the properties of linear transformations and groups. It covers the preservation of adjacency by compositions of permutations, the structure of vector spaces, and the dihedral group. The lecture also explores the preservation of adjacency by bijections and the conditions for forming subgroups. Additionally, it delves into the generation of sub-groups and the smallest generating set within a group.