Nilpotent Groups

Rudiments.- The upper central series.- Tensor products and the lower central series.- Idempotent radicals on the category of nilpotent groups.- Groups with abelian central quotient.- The Hall-Petresco formula and residual boundedness.- Completions and the structure of complete groups.- Localization.- Nilpotent actions, Kolchin's theorem, and engel conditions.- Nilpotent groups admitting exponents in a ring.- Unipotent representations and Malcev completions of R-groups.- The Malcev correspondence.