Finite Presentability of S-Arithmetic Groups. Compact Presentability of Solvable Groups PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Finite Presentability of S-Arithmetic Groups. Compact Presentability of Solvable Groups PDF full book. Access full book title Finite Presentability of S-Arithmetic Groups. Compact Presentability of Solvable Groups by Herbert Abels. Download full books in PDF and EPUB format.
Author: Herbert Abels
Publisher: Springer
ISBN: 3540471987
Category : Mathematics
Languages : en
Pages : 184
Get Book Here
Book Description
The problem of determining which S-arithmetic groups have a finite presentation is solved for arbitrary linear algebraic groups over finite extension fields of #3. For certain solvable topological groups this problem may be reduced to an analogous problem, that of compact presentability. Most of this monograph deals with this question. The necessary background material and the general framework in which the problem arises are given partly in a detailed account, partly in survey form. In the last two chapters the application to S-arithmetic groups is given: here the reader is assumed to have some background in algebraic and arithmetic group. The book will be of interest to readers working on infinite groups, topological groups, and algebraic and arithmetic groups.
Author: Herbert Abels
Publisher: Springer
ISBN: 3540471987
Category : Mathematics
Languages : en
Pages : 184
Get Book Here
Book Description
The problem of determining which S-arithmetic groups have a finite presentation is solved for arbitrary linear algebraic groups over finite extension fields of #3. For certain solvable topological groups this problem may be reduced to an analogous problem, that of compact presentability. Most of this monograph deals with this question. The necessary background material and the general framework in which the problem arises are given partly in a detailed account, partly in survey form. In the last two chapters the application to S-arithmetic groups is given: here the reader is assumed to have some background in algebraic and arithmetic group. The book will be of interest to readers working on infinite groups, topological groups, and algebraic and arithmetic groups.
Author: Lizhen Ji
Publisher: American Mathematical Soc.
ISBN: 0821848666
Category : Mathematics
Languages : en
Pages : 282
Get Book Here
Book Description
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
Author: E. F. Robertson
Publisher: Cambridge University Press
ISBN: 9780521338547
Category : Mathematics
Languages : en
Pages : 376
Get Book Here
Book Description
A current picture of progress and research in group theory is provided by five leading group theorists Bachmuth, Baumslag, Neumann, Roseblade and Tits.
Author: Vladimir Platonov
Publisher: Academic Press
ISBN: 0080874592
Category : Mathematics
Languages : en
Pages : 629
Get Book Here
Book Description
This 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.
Author: Vladimir Platonov
Publisher: Cambridge University Press
ISBN: 1009380656
Category : Mathematics
Languages : en
Pages : 380
Get Book Here
Book Description
The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.
Author: Peter Abramenko
Publisher: Springer
ISBN: 3540495703
Category : Mathematics
Languages : en
Pages : 131
Get Book Here
Book Description
This book is addressed to mathematicians and advanced students interested in buildings, groups and their interplay. Its first part introduces - presupposing good knowledge of ordinary buildings - the theory of twin buildings, discusses its group-theoretic background (twin BN-pairs), investigates geometric aspects of twin buildings and applies them to determine finiteness properties of certain S-arithmetic groups. This application depends on topological properties of some subcomplexes of spherical buildings. The background of this problem, some examples and the complete solution for all "sufficiently large" classical buildings are covered in detail in the second part of the book.
Author: Enrique Ramirez de Arellano
Publisher: Springer
ISBN: 3540469133
Category : Mathematics
Languages : en
Pages : 192
Get Book Here
Book Description
Author: Peter H. Kropholler
Publisher: Cambridge University Press
ISBN: 052163556X
Category : Mathematics
Languages : en
Pages : 332
Get Book Here
Book Description
This volume reflects the fruitful connections between group theory and topology. It contains articles on cohomology, representation theory, geometric and combinatorial group theory. Some of the world's best known figures in this very active area of mathematics have made contributions, including substantial articles from Ol'shanskii, Mikhajlovskii, Carlson, Benson, Linnell, Wilson and Grigorchuk, which will be valuable reference works for some years to come. Pure mathematicians working in the fields of algebra, topology, and their interactions, will find this book of great interest.
Author: Stefan Hildebrandt
Publisher: Springer
ISBN: 3540460241
Category : Mathematics
Languages : en
Pages : 433
Get Book Here
Book Description
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
Author: Vladimir Platonov
Publisher: Cambridge University Press
ISBN: 052111361X
Category : Mathematics
Languages : en
Pages : 379
Get Book Here
Book Description
The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.
