In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.

1. An Introduction to Compact P-adic Lie groups By Benjamin
Klopsch
2. From Finite P-adic to Compact Lie groups
3. Basic Notions and Facts from point-set topology
4. First series of exercises
5. Powerful groups, profinite groups and pro-p groups
6. Second series of exercises
7. Uniformly powerful pro-p groups and Zp-Lie Lattices
8. The group GLd (Zp), just-infinite pro-p groups and the lie
9. Third series of exercise
10. Representations of compact P-adic Lie groups