Torsion and Divisibility in Group Theory

This lecture delves into the relationship between p-torsion and p-divisibility, focusing on exact sequences involving p-groups. It explores the implications when two out of three groups A, B, and C are p-groups, shedding light on the third one. The lecture also discusses the concept of exact sequences of abelian groups and the consequences of p-divisibility. Through various examples, the instructor illustrates scenarios where p-divisibility does not necessarily imply divisibility. The lecture concludes by examining the extension of a group G into a functor, emphasizing the construction and properties of the extension. The discussion also touches upon the injectivity of certain mappings and the implications of p-divisibility on group elements.