Dihedral Group: Symmetries and Cosets

This lecture covers the definition and presentation of the dihedral group, focusing on the symmetries of a regular n-gon. It explains the concept of normal subgroups and cosets, emphasizing Lagrange's theorem. The presentation includes the generators and relations of the dihedral group, as well as the properties of reflections and rotations. The lecture also discusses the number of elements in a dihedral group and the structure of left cosets relative to a given subgroup.