P-Adic and p-cotorsion completions of nilpotent groups

Abstract

The theory of cotorsion Abelian groups is extended to the category of nilpotent groups, and applications are given to the theory of p-adic completions and exactness properties of the p-adic completion functor. The p-cotorsion completion functor was first extended from Abelian to nilpotent groups by Bousfield and Kan, who defined and studied it using topological methods. We develop the theory group-theoretically, and additional results and applications.