Groups, Combinatorics and Geometry

Groups, Combinatorics and Geometry
Author: Martin W. Liebeck
Publisher: Cambridge University Press
Total Pages: 505
Release: 1992-09-10
Genre: Mathematics
ISBN: 0521406854

This volume contains a collection of papers on the subject of the classification of finite simple groups.

Topics in Groups and Geometry

Topics in Groups and Geometry
Author: Tullio Ceccherini-Silberstein
Publisher: Springer Nature
Total Pages: 468
Release: 2022-01-01
Genre: Mathematics
ISBN: 3030881091

This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

Geometric Combinatorics

Geometric Combinatorics
Author: Ezra Miller
Publisher: American Mathematical Soc.
Total Pages: 705
Release: 2007
Genre: Combinatorial analysis
ISBN: 0821837362

Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.

Groups, Combinatorics & Geometry

Groups, Combinatorics & Geometry
Author: A. A. Ivanov
Publisher: World Scientific
Total Pages: 347
Release: 2003
Genre: Mathematics
ISBN: 9812383123

"This book contains the proceedings of the L.M.S. Durham Symposium on Groups, Geometry and Combinatorics, July 16-26, 2001"--P. v.

Combinatorial and Geometric Group Theory

Combinatorial and Geometric Group Theory
Author: Oleg Bogopolski
Publisher: Springer Science & Business Media
Total Pages: 318
Release: 2011-01-28
Genre: Mathematics
ISBN: 3764399112

This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.

Combinatorics of Coxeter Groups

Combinatorics of Coxeter Groups
Author: Anders Bjorner
Publisher: Springer Science & Business Media
Total Pages: 371
Release: 2006-02-25
Genre: Mathematics
ISBN: 3540275967

Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups

Geometric Group Theory

Geometric Group Theory
Author: Clara Löh
Publisher: Springer
Total Pages: 390
Release: 2017-12-19
Genre: Mathematics
ISBN: 3319722549

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Office Hours with a Geometric Group Theorist

Office Hours with a Geometric Group Theorist
Author: Matt Clay
Publisher: Princeton University Press
Total Pages: 456
Release: 2017-07-11
Genre: Mathematics
ISBN: 1400885396

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincaré, Felix Klein, J.H.C. Whitehead, and Max Dehn. Office Hours with a Geometric Group Theorist brings together leading experts who provide one-on-one instruction on key topics in this exciting and relatively new field of mathematics. It's like having office hours with your most trusted math professors. An essential primer for undergraduates making the leap to graduate work, the book begins with free groups—actions of free groups on trees, algorithmic questions about free groups, the ping-pong lemma, and automorphisms of free groups. It goes on to cover several large-scale geometric invariants of groups, including quasi-isometry groups, Dehn functions, Gromov hyperbolicity, and asymptotic dimension. It also delves into important examples of groups, such as Coxeter groups, Thompson's groups, right-angled Artin groups, lamplighter groups, mapping class groups, and braid groups. The tone is conversational throughout, and the instruction is driven by examples. Accessible to students who have taken a first course in abstract algebra, Office Hours with a Geometric Group Theorist also features numerous exercises and in-depth projects designed to engage readers and provide jumping-off points for research projects.

Algebraic Combinatorics and Coinvariant Spaces

Algebraic Combinatorics and Coinvariant Spaces
Author: Francois Bergeron
Publisher: CRC Press
Total Pages: 227
Release: 2009-07-06
Genre: Mathematics
ISBN: 1439865078

Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and