Blocks of Finite Groups and Their Invariants

Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the clas...

Full description

Saved in:
Bibliographic Details
Main Author Sambale, Benjamin
Format eBook Book
LanguageEnglish
Published Cham Springer Nature 2014
Springer
Springer International Publishing AG
Springer International Publishing
Edition1
SeriesLecture Notes in Mathematics
Subjects
Algebra & number theory
Blocks (Group theory)
Finite groups
Group Theory and Generalizations
Invariants
Mathematics
Mathematics and Statistics
Online AccessGet full text

Cover

Abstract Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.
AbstractList Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.
Author Sambale, Benjamin
Author_xml – sequence: 1
  fullname: Sambale, Benjamin
BackLink https://cir.nii.ac.jp/crid/1130282271337461120$$DView record in CiNii
BookMark eNpdkE9v1DAQxQ20iG3ZD8AtqpAQEqYz_u8jXbWlUiUu5Ww5XqcbNthLnJavj7PhApcZ6c3vPc3MGTlJOUVC3iF8RgB9abWhnHK0FBmAovIFWVeNV-UoyJdkhQo1tcqyV__NTsiqZkhqBBen5IwBCiuFAfOarIxVBlFK_oasS_kBAMiN4pqvyKerIYd9aXLX3PSpn2JzO-anQ2l82jYPu9iPzV169mPv01TektPODyWu__Zz8v3m-mHzld5_u73bfLmnnhmtgUoruk6YrffGsiAUYhdaLSOwrkMFEqFtt1FZiR60aUUbWOAsKi9CsMbwc_JxyfVlH3-XXR6m4p6H2Oa8L-6fsyt7ubDlMPbpMY5uoRDc_NSZdtxV3h0NbnZ8WByHMf96imVyx-AQ0zT6wV1fbaSsSzBdyfcLmfrehX6uiByYYUwj53q-jEHFLhYs-OKHirmfOeXH0R92xUkBhnHD_wBdloHw
ContentType eBook
Book
Copyright Springer International Publishing Switzerland 2014
Copyright_xml – notice: Springer International Publishing Switzerland 2014
DBID I4C
RYH
DEWEY 512
DOI 10.1007/978-3-319-12006-5
DatabaseName Casalini Torrossa eBooks Institutional Catalogue
CiNii Complete
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 9783319120065
3319120069
EISSN 1617-9692
Edition 1
2014
ExternalDocumentID 9783319120065
330178
EBC5588327
BB17484026
5408238
GroupedDBID 0DA
0DF
2HY
38.
A0Z
A3-
AABBV
AACUA
AAVAM
ABBVZ
ABMNI
ACTXJ
AEJLV
AEKFX
AETDV
AEZAY
AHJUR
ALMA_UNASSIGNED_HOLDINGS
ANZUN
AZZ
BBABE
BZAQK
CZZ
I4C
IEZ
LDK
SBO
TPJZQ
RYH
-GH
-~C
1SB
29L
2HD
5GY
ABZEH
ACGFS
ACNCT
AENEX
AHDLI
DU5
RIG
RSU
SVGTG
UQL
VI1
WH7
ID FETCH-LOGICAL-a28770-594ff48daa892c4611fcb75e02ff160510bbde6951a078b4bc2c32e6a4cc9883
IEDL.DBID LDK
ISBN 9783319120065
3319120069
3319120050
9783319120058
ISSN 0075-8434
IngestDate Fri Nov 08 04:07:40 EST 2024
Tue Jul 29 20:32:04 EDT 2025
Fri May 30 23:27:24 EDT 2025
Thu Jun 26 22:16:02 EDT 2025
Tue Mar 04 07:37:43 EST 2025
IsPeerReviewed true
IsScholarly true
LCCN 2014954808
LCCallNum_Ident QA
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a28770-594ff48daa892c4611fcb75e02ff160510bbde6951a078b4bc2c32e6a4cc9883
Notes Includes bibliographical references (p. 229-239) and index
OCLC 896811553
PQID EBC5588327
PageCount 246
ParticipantIDs askewsholts_vlebooks_9783319120065
springer_books_10_1007_978_3_319_12006_5
proquest_ebookcentral_EBC5588327
nii_cinii_1130282271337461120
casalini_monographs_5408238
PublicationCentury 2000
PublicationDate [2014]
PublicationDateYYYYMMDD 2014-01-01
PublicationDate_xml – year: 2014
  text: [2014]
PublicationDecade 2010
PublicationPlace Cham
PublicationPlace_xml – name: Netherlands
– name: Cham
PublicationSeriesTitle Lecture Notes in Mathematics
PublicationSeriesTitleAlternate Lect.Notes Mathematics
PublicationYear 2014
Publisher Springer Nature
Springer
Springer International Publishing AG
Springer International Publishing
Publisher_xml – name: Springer Nature
– name: Springer
– name: Springer International Publishing AG
– name: Springer International Publishing
RelatedPersons Wienhard, Anna
Khoshnevisan, Davar
Kontoyiannis, Ioannis
Stroppel, Catharina
De Lellis, Camillo
Serfaty, Sylvia
Teissier, Bernard
di Bernardo, Mario
Figalli, Alessio
Podolskij, Mark
Morel, J.-M.
Lugosi, Gabor
RelatedPersons_xml – sequence: 1
  givenname: J.-M.
  surname: Morel
  fullname: Morel, J.-M.
– sequence: 2
  givenname: Bernard
  surname: Teissier
  fullname: Teissier, Bernard
– sequence: 3
  givenname: Camillo
  surname: De Lellis
  fullname: De Lellis, Camillo
– sequence: 4
  givenname: Mario
  surname: di Bernardo
  fullname: di Bernardo, Mario
– sequence: 5
  givenname: Alessio
  surname: Figalli
  fullname: Figalli, Alessio
– sequence: 6
  givenname: Davar
  surname: Khoshnevisan
  fullname: Khoshnevisan, Davar
– sequence: 7
  givenname: Ioannis
  surname: Kontoyiannis
  fullname: Kontoyiannis, Ioannis
– sequence: 8
  givenname: Gabor
  surname: Lugosi
  fullname: Lugosi, Gabor
– sequence: 9
  givenname: Mark
  surname: Podolskij
  fullname: Podolskij, Mark
– sequence: 10
  givenname: Sylvia
  surname: Serfaty
  fullname: Serfaty, Sylvia
– sequence: 11
  givenname: Catharina
  surname: Stroppel
  fullname: Stroppel, Catharina
– sequence: 12
  givenname: Anna
  surname: Wienhard
  fullname: Wienhard, Anna
SSID ssj0001386373
ssj0025440
Score 2.5791607
Snippet Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical...
SourceID askewsholts
springer
proquest
nii
casalini
SourceType Aggregation Database
Publisher
SubjectTerms Algebra & number theory
Blocks (Group theory)
Finite groups
Group Theory and Generalizations
Invariants
Mathematics
Mathematics and Statistics
TableOfContents Index
Intro -- Introduction -- Contents -- List of Tables -- Part I Fundamentals -- Chapter 1 Definitions and Facts -- 1.1 Group Algebras and Blocks -- 1.2 Defect Groups and Characters -- 1.3 Brauer's Main Theorems -- 1.4 Covering and Domination -- 1.5 Fusion Systems -- 1.6 Subsections and Contributions -- 1.7 Centrally Controlled Blocks -- 1.8 Lower Defect Groups -- Chapter 2 Open Conjectures -- Part II General Results and Methods -- Chapter 3 Quadratic Forms -- Chapter 4 The Cartan Method -- 4.1 An Inequality -- 4.2 An Algorithm -- 4.3 The Inverse Cartan Method -- 4.4 More Inequalities -- Chapter 5 A Bound in Terms of Fusion Systems -- 5.1 The Case p=2 -- 5.2 The Case p&gt -- 2 -- Chapter 6 Essential Subgroups and Alperin's Fusion Theorem -- Chapter 7 Reduction to Quasisimple Groups and the Classification -- 7.1 Fong Reductions -- 7.2 Extensions of Nilpotent Blocks -- 7.3 Components -- 7.4 The Classification of the Finite Simple Groups -- 7.5 Blocks of p-Solvable Groups -- Part III Applications -- Chapter 8 Metacyclic Defect Groups -- 8.1 The Case p=2 -- 8.2 The Case p&gt -- 2 -- 8.2.1 Metacyclic, Minimal Non-abelian Defect Groups -- 8.2.2 One Family for p=3 -- Chapter 9 Products of Metacyclic Groups -- 9.1 D_2^n x C_2^m -- 9.2 D_2^n ∗ C_2^m -- 9.3 Q_2^n x C_2^m -- 9.4 SD_2^n x C_2^m -- Chapter 10 Bicyclic Groups -- 10.1 Fusion Systems -- 10.1.1 The Case P Non-cyclic -- 10.1.2 The Case P Cyclic -- 10.2 Blocks -- Chapter 11 Defect Groups of p-Rank 2 -- Chapter 12 Minimal Non-abelian Defect Groups -- 12.1 The Case p=2 -- 12.2 The Case p&gt -- 2 -- Chapter 13 Small Defect Groups -- 13.1 Results on the k(B)-Conjecture -- 13.2 2-Blocks of Defect 5 -- 13.3 Minimal Non-metacyclic Defect Groups -- Chapter 14 Abelian Defect Groups -- 14.1 The Brauer-Feit Bound -- 14.2 Abelian Groups of Small Rank -- Chapter 15 Blocks with Few Characters -- References
Title Blocks of Finite Groups and Their Invariants
URI http://digital.casalini.it/9783319120065
https://cir.nii.ac.jp/crid/1130282271337461120
https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=5588327
http://link.springer.com/10.1007/978-3-319-12006-5
https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9783319120065
Volume 2127
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1La9wwEB7a5NK9pE_qpimm9NBDHWy9LF-TZklS0tMGchOSLMGyxYF6k0N_fWfk1eZBDu3FYCPk8Yw1D30zI4AvrrFKRSErH2JfiRhZZV3sqi4G3vPaqpCSMS9-qtNLcX4lrzZ13GPOds-QZNLUudhtwvGp5qZJYbB8DrucUDPqIPn9x93GCteKt1t1TC24pjqUVlZacDrnieMsNIncNH3a3uuMez71vhnM7LhC1YNqaT2SHbOjpfJFNEvDcvnARX2EqiZjNd-DRf7MKUdldXizdof-z6MOkP_Jh5ewG6gw4hU8C8NrmF1s-72Ob-DbEdrE1Vhex3K-JC-2THtaY2mHvlwQFlGeDbcYllPWzVu4nJ8sjk-rzTkMlcV4qq0r2aEQhe6t1R3zQjVN9K6VoWYxNoqWtXN9UOisWfQ4nHCeec6CssL7Tmv-DnaG6yG8h5L1WukmaNVjZImxFI6te9big6B8w0IBn-_x2Nz-SpDxaO4JSckC9jPrDa7VqbX3aCSdnc11AQcoDeOXdG0Il0UfiELxlghndQFllpNJs2-yYM3J0bGUSC1rC_iaWW-m9-fmzkiH4QYpMYkUIz_8-9B9eIHelpj2bz7Czvr3TThAj2btPqU_-C_1fN7u
linkProvider Springer Nature
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9QwEB5Be4C9lKdISyFCHDiQKvErzrWlqy3t9rSVerNsx5ZWW6US3vbAr2fsrJdScYBLpESWM5mJZ77xPAzw2TRaCM94ZZ3vK-Y9qbTxXdV5R3taa-FSMub8Usyu2Pdrfr2p4w452z2HJJOmzsVuYxw_1tw0yQ3mT2GXEUTgsYPkt_PfGytUCtpu1XFswTXWobS8kozGc54ozhIn4ZumT9t7meOef3vfBCY6rFD1oFpah2jHdNCxfBHN0rBc_gFRH0VVk7Ga7sEif-aYo7I6ulubI_vzUQfI_-TDC9h1sTDiJTxxwyuYzLf9XsNr-HqMNnEVyltfTpcRxZZpTyuUeujLRYxFlGfDPbrlMevmDVxNTxcns2pzDkOl0Z9q64p3KEQme61lRywTTeOtabmrifeNiMvamN4JBGsaEYdhxhJLiROaWdtJSd_CznA7uHdQkl4K2TgpevQs0ZfCsXVPWnzghG2IK-DTAx6r-5sUMg7qgZAEL-Ags17hWh1bewfF49nZVBZwiNJQdhmvTYzLIgaKrngbCSd1AWWWk0qzb7Jg1enxCedILWkL-JJZr8b35-bOSIeiCilRiRTF9_996Ed4NlvML9TF2eX5ATxH5MXGvZz3sLP-cecOEd2szYf0N_8ChLvh1g
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=Blocks+of+finite+groups+and+their+invariants&rft.au=Sambale%2C+Benjamin&rft.date=2014-01-01&rft.pub=Springer&rft.isbn=9783319120058&rft_id=info:doi/10.1007%2F978-3-319-12006-5&rft.externalDocID=BB17484026
thumbnail_m http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97833191%2F9783319120065.jpg
thumbnail_s http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fmedia.springernature.com%2Fw306%2Fspringer-static%2Fcover-hires%2Fbook%2F978-3-319-12006-5