Topics In Infinite Group Theory
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Topics in Infinite Group Theory
Author: Benjamin Fine
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2024-11-18
This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems. New edition now includes the topics on universal free groups, quasiconvex subgroups and hyperbolic groups, and also Stallings foldings and subgroups of free groups. New results on groups of F-types are added.
Topics in Infinite Group Theory
This book gives an overview of several topics in infinite group theory. The first part of the book deals with Nielsen methods and introduces in detail many results, examples, and applications that are useful to understand the following parts. The second part focuses on fundamental groups, including applications such as the Reidemeister-Schreier method, whereas the third part focuses on hyperbolic groups.
Lectures on Profinite Topics in Group Theory
Author: Benjamin Klopsch
language: en
Publisher: Cambridge University Press
Release Date: 2011-02-10
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.