Divisibility and Torsion

This lecture covers the concepts of divisibility and torsion in the context of group theory, focusing on defining a functor D: Abelian Groups -> Abelian Groups that preserves divisibility. The instructor explains the decomposition of cyclic groups, the notion of divisible elements, and the construction of the functor D. The lecture delves into the properties of D, its relation to Hom functors, and the divisibility of elements in Abelian groups. Various approaches to defining D and verifying its properties are discussed, emphasizing the significance of divisibility and torsion in group structures.