The Resource Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)

Subgroup Growth, by Alexander Lubotzky, Dan Segal, (electronic resource)

Label
Subgroup Growth
Title
Subgroup Growth
Statement of responsibility
by Alexander Lubotzky, Dan Segal
Creator
Contributor
Subject
Genre
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 so-called 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 "non-commutative arithmetic", with applications to the study of lattices in Lie groups. Another kind of non-commutative arithmetic arises with the introduction of subgroup-counting zeta functions; these fascinating and mysterious zeta functions have remarkable applications both to the "arithmetic of subgroup growth" and to the classification of finite p-groups. 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", 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
Member of
Cataloging source
AU@
http://library.link/vocab/creatorName
Lubotzky, Alexander
Dewey number
512
Index
no index present
LC call number
QA150-272
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)
Link
http://dx.doi.org/10.1007/978-3-0348-8965-0
Instantiates
Publication
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 -- Pro-p 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: p-adic 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
10.1007/978-3-0348-8965-0
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)
Link
http://dx.doi.org/10.1007/978-3-0348-8965-0
Publication
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 -- Pro-p 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: p-adic 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
10.1007/978-3-0348-8965-0
Quality assurance targets
unknown
Reformatting quality
access
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)851797751
  • (OCoLC)ocn851797751

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