Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth
studies the distribution of subgroups of finite index in a group as a function of the index. In …

The central concept in this monograph is that of a soluble group-a group which is built up
from abelian groups by repeatedly forming group extensions. It covers all the major areas …

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 …

It has become somewhat of a cottage industry over the last fifteen years to understand the
rate of growth of the number of subgroups of finite index in a group G. Although the story …

We introduce a new method to compute explicit formulae for various zeta functions
associated to groups and rings. The specific form of these formulae enables us to deduce …

Thestudyofthesubgroupgrowthofin? nitegroupsisanareaofmathematical research that has
grown rapidly since its inception at the Groups St. Andrews conferencein1985. Ithasbecomearichtheoryrequiringtoolsfroma …

We develop a theory of average sizes of kernels of generic matrices with support constraints
defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups …

We present a survey of results related to Milnor's problem on group growth. We discuss the
cases of polynomial growth and exponential but not uniformly exponential growth; the main …

We prove that the theory of the p-adics Qp admits elimination of imaginaries provided we
add a sort for GLn (Qp)/GLn (Zp) for each n. We also prove that the elimination of …

We survey applications of quantifier elimination to number theory and algebraic geometry,
focusing on results of the last 15 years. We start with the applications of p-adic quantifier …