Classification of Extensions

This lecture covers the classification of extensions in group theory, focusing on split extensions and semi-direct products. The instructor explains the concept of a split extension and its equivalence to a semi-direct product. The lecture delves into the properties of extensions, such as group homomorphisms and conjugation. It also discusses the conditions for an extension to be considered split and the bijection between conjugacy classes. The presentation concludes with the implications of factor sets and the role of 2-cocycles in determining the equivalence of extensions.