Finite Abelian Groups

This lecture covers Cauchy's theorem, the classification of simple finite abelian groups, direct product properties, and the classification of finite abelian groups based on elementary divisors and invariant factors. It also discusses the Orbit-Stabilizer theorem, normal subgroups, conjugacy classes, and examples of finite abelian groups. The lecture concludes with the classification of all possible finite abelian groups and the properties of direct product groups.