Pro-finite Lie rings and p-adic Lie algebras.

摘要

Pro-finite Lie rings are the Lie theoretic analogue of pro-finite groups. Pro-finite group theory has often made use of Lie theoretic techniques. This thesis exploits the relationship between groups and Lie rings in the opposite direction, providing a systematic study of pro-finite Lie rings, with the intention of furthering our understanding of both Lie rings and groups.;Keywords. Lie ring, p-adic Lie algebra, pro-finite group, pro-p group, p-adic analytic group.;In particular, this thesis provides a detailed study of the class of Lie Zp -algebras we call pro-p Lie rings (the Lie theoretic analogue to pro-p groups), studies the relationship between the algebraic structure and topology of pro-finite Lie rings, and provides a positive solution to the Kurosh problem for pro-finite Lie rings.