The first edition of this book was the indispensable reference for researchers in the theory of
pro-p groups. In this second edition the presentation has been improved and important new …

In this chapter we define and investigate the class of branch groups. This class has only
recently been defined, but the first examples of groups with a branch structure appeared at …

This book offers to study locally compact groups from the point of view of appropriate metrics
that can be defined on them, in other words to study" Infinite groups as geometric objects" …

Publisher Summary This chapter discusses the abstract branch groups. There are two new
approaches to the definition of a branch group. The first one is purely algebraic, defining …

The idea of self-similarity is one of the most fundamental in the modern mathematics. The
notion of “renormalization group”, which plays an essential role in quantum field theory …

We show that every n\, *\, nn× n matrix is generically a product of ⌊ n/2 ⌋+ 1⌊ n/2⌋+ 1
Toeplitz matrices and always a product of at most 2 n+ 5 2 n+ 5 Toeplitz matrices. The same …

We study the subgroup structure, Hecke algebras, quasi-regular representations, and
asymptotic properties of some fractal groups of branch type. We introduce parabolic …

As interest in pro-p groups has grown, so has interest in the Nottingham group. Known to
number theorists as the group of wild automorphisms of the local field lFq «t»(where q= pe) …

A systematic description is given of properties of the group J (k) of formal power series in
one variable with coefficients in a commutative unitary ring k. This topological group has …

If $ G $ is a GGS-group defined over a $ p $-adic tree, where $ p $ is an odd prime, we
calculate the order of the congruence quotients $ G_n= G/\mathrm {Stab} _G (n) $ for every …