The Congruence Subgroup Problem - An Elementary Approach Aimed at Applications
Author: B. Sury
Publisher: Springer
Published: 2003-01-01
Total Pages: 315
ISBN-13: 9386279193
DOWNLOAD EBOOKPosts
Solution of the Congruence Subgroup Problem for SLn (n [is Greater Than Or Equal To] 3) and Sp2n (n [is Greater Than Or Equal To] 2)
Author: Hyman Bass
Publisher:
Published: 1967
Total Pages: 278
ISBN-13:
DOWNLOAD EBOOKSubgroup Growth
Author: Alexander Lubotzky
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 463
ISBN-13: 3034889658
DOWNLOAD EBOOKAward-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 last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.
Handbook of Teichmüller Theory
Author: Athanase Papadopoulos
Publisher: European Mathematical Society
Published: 2007
Total Pages: 876
ISBN-13: 9783037191033
DOWNLOAD EBOOKThe subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.
Exercises in Cellular Automata and Groups
Author: Tullio Ceccherini-Silberstein
Publisher: Springer Nature
Published: 2023-11-01
Total Pages: 638
ISBN-13: 3031103912
DOWNLOAD EBOOKThis book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk
The Abel Prize
Author: Helge Holden
Publisher: Springer Science & Business Media
Published: 2009-12-01
Total Pages: 325
ISBN-13: 3642013732
DOWNLOAD EBOOKThe book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com .
Profinite Groups
Author: Luis Ribes
Publisher: Springer Science & Business Media
Published: 2013-04-09
Total Pages: 441
ISBN-13: 3662040972
DOWNLOAD EBOOKThis self-contained book serves both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. It contains complete and clear proofs for most results, many of which appear here in book form for the first time. Suitable as a basis for courses.
The Congruence Subgroup Problem -
Author: B. Sury
Publisher: Hindustan Book Agency and Indian National Science Academy
Published: 2003
Total Pages: 328
ISBN-13:
DOWNLOAD EBOOK"This is an elementary introduction to the congruence subgroup problem, a problem which deals with number theoretic properties of groups defined arithmetically." "The novelty and, indeed, the goal of this book is to present some applications to group theory as well as to number theory which have emerged in the last fifteen years." "No knowledge of algebraic groups is assumed and the choice of the examples discussed seeks to convey that even these special cases give interesting applications." "The book is intended for beginning graduate students. Many exercises are given."--BOOK JACKET.
Algebraic Groups and Number Theory
Author: Vladimir Platonov
Publisher: Academic Press
Published: 1993-12-07
Total Pages: 629
ISBN-13: 0080874592
DOWNLOAD EBOOKThis milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.
Problems on Mapping Class Groups and Related Topics
Author: Benson Farb
Publisher: American Mathematical Soc.
Published: 2006-09-12
Total Pages: 384
ISBN-13: 0821838385
DOWNLOAD EBOOKThe appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
