Borrow it
 Architecture Library
 Bizzell Memorial Library
 Boorstin Collection
 Chinese Literature Translation Archive
 Engineering Library
 Fine Arts Library
 Harry W. Bass Business History Collection
 History of Science Collections
 John and Mary Nichols Rare Books and Special Collections
 Library Service Center
 Price College Digital Library
 Western History Collections
The Resource Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)
Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)
Resource Information
The item Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 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. For example the socalled PSG Theorem, proved in Chapter 5, characterizes the groups of polynomial subgroup growth as those which are virtually soluble of finite rank. A key element in the proof is the growth of congruence subgroups in arithmetic groups, a new kind of "noncommutative arithmetic", with applications to the study of lattices in Lie groups. Another kind of noncommutative arithmetic arises with the introduction of subgroupcounting zeta functions; these fascinating and mysterious zeta functions have remarkable applications both to the "arithmetic of subgroup growth" and to the classification of finite pgroups. 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 padic model theory. Relevant aspects of such topics are explained in selfcontained "windows", making the book accessible to a wide mathematical readership. The book concludes with over 60 challenging open problems that will stimulate further research in this rapidly growing subject
 Language
 eng
 Extent
 1 online resource (xxii, 454 pages).
 Contents

 Preface
 Notation
 Introduction and Overview
 Basic Techniques of Subgroup Counting
 Free Groups
 Groups with Exponential Subgroup Growth
 Prop Groups
 Finitely Generated Groups with Polynomial Subgroup Growth
 Congruence Subgroups
 The Generalized Congruence Subgroup Problem
 Linear Groups
 Soluble Groups
 Profinite Groups with Polynomial Subgroup Growth
 Probabilistic Methods
 Other Growth Conditions
 The Growth Spectrum
 Explicit Formulas and Asymptotics
 Zeta Functions I: Nilpotent Groups
 Zeta Functions II: padic Analytic Groups
 Windows
 Open Problems
 Bibliography
 Index
 Isbn
 9783034889650
 Label
 Subgroup Growth
 Title
 Subgroup Growth
 Statement of responsibility
 by Alexander Lubotzky, Dan Segal
 Language
 eng
 Summary
 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. For example the socalled PSG Theorem, proved in Chapter 5, characterizes the groups of polynomial subgroup growth as those which are virtually soluble of finite rank. A key element in the proof is the growth of congruence subgroups in arithmetic groups, a new kind of "noncommutative arithmetic", with applications to the study of lattices in Lie groups. Another kind of noncommutative arithmetic arises with the introduction of subgroupcounting zeta functions; these fascinating and mysterious zeta functions have remarkable applications both to the "arithmetic of subgroup growth" and to the classification of finite pgroups. 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 padic model theory. Relevant aspects of such topics are explained in selfcontained "windows", making the book accessible to a wide mathematical readership. The book concludes with over 60 challenging open problems that will stimulate further research in this rapidly growing subject
 Cataloging source
 AU@
 http://library.link/vocab/creatorName
 Lubotzky, Alexander
 Dewey number
 512
 Index
 no index present
 LC call number
 QA150272
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Segal, Dan
 Series statement
 Progress in Mathematics
 Series volume
 212
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Group theory
 Number theory
 Algebra
 Group theory
 Mathematics
 Number theory
 Label
 Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)
 Antecedent source
 file reproduced from original
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 mixed
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  Notation  Introduction and Overview  Basic Techniques of Subgroup Counting  Free Groups  Groups with Exponential Subgroup Growth  Prop Groups  Finitely Generated Groups with Polynomial Subgroup Growth  Congruence Subgroups  The Generalized Congruence Subgroup Problem  Linear Groups  Soluble Groups  Profinite Groups with Polynomial Subgroup Growth  Probabilistic Methods  Other Growth Conditions  The Growth Spectrum  Explicit Formulas and Asymptotics  Zeta Functions I: Nilpotent Groups  Zeta Functions II: padic Analytic Groups  Windows  Open Problems  Bibliography  Index
 Dimensions
 unknown
 Extent
 1 online resource (xxii, 454 pages).
 File format
 unknown
 Form of item
 online
 Isbn
 9783034889650
 Isbn Type
 (electronic bk.)
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783034889650
 Quality assurance targets
 unknown
 Reformatting quality
 access
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)851797751
 (OCoLC)ocn851797751
 Label
 Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)
 Antecedent source
 file reproduced from original
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 mixed
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  Notation  Introduction and Overview  Basic Techniques of Subgroup Counting  Free Groups  Groups with Exponential Subgroup Growth  Prop Groups  Finitely Generated Groups with Polynomial Subgroup Growth  Congruence Subgroups  The Generalized Congruence Subgroup Problem  Linear Groups  Soluble Groups  Profinite Groups with Polynomial Subgroup Growth  Probabilistic Methods  Other Growth Conditions  The Growth Spectrum  Explicit Formulas and Asymptotics  Zeta Functions I: Nilpotent Groups  Zeta Functions II: padic Analytic Groups  Windows  Open Problems  Bibliography  Index
 Dimensions
 unknown
 Extent
 1 online resource (xxii, 454 pages).
 File format
 unknown
 Form of item
 online
 Isbn
 9783034889650
 Isbn Type
 (electronic bk.)
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783034889650
 Quality assurance targets
 unknown
 Reformatting quality
 access
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)851797751
 (OCoLC)ocn851797751
Library Locations

Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 97.445050



Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 97.447906

Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 97.445050

Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 97.448244

Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 97.447906

John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 97.447906


Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 97.448244

Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 97.445414
Embed (Experimental)
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/SubgroupGrowthbyAlexanderLubotzkyDan/VjDkUF3fuwE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/SubgroupGrowthbyAlexanderLubotzkyDan/VjDkUF3fuwE/">Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/SubgroupGrowthbyAlexanderLubotzkyDan/VjDkUF3fuwE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/SubgroupGrowthbyAlexanderLubotzkyDan/VjDkUF3fuwE/">Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>