The Resource Abstract Root Subgroups and Simple Groups of Lie-Type, by Franz G. Timmesfeld, (electronic resource)

Abstract Root Subgroups and Simple Groups of Lie-Type, by Franz G. Timmesfeld, (electronic resource)

Label
Abstract Root Subgroups and Simple Groups of Lie-Type
Title
Abstract Root Subgroups and Simple Groups of Lie-Type
Statement of responsibility
by Franz G. Timmesfeld
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
It was already in 1964 [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. This question is quite natural, since the class of transpositions of a symmetric group possesses this property. Namely the order of the product (ij)(kl) is 1, 2 or 3 according as {i,j} n {k,l} consists of 2,0 or 1 element. In fact, if I{i,j} n {k,I}1 = 1 and j = k, then (ij)(kl) is the 3-cycle (ijl). After the preliminary papers [Fis66] and [Fis64] he succeeded in [Fis71J, [Fis69] to classify all finite "nearly" simple groups generated by such a class of 3-transpositions, thereby discovering three new finite simple groups called M(22), M(23) and M(24). But even more important than his classification theorem was the fact that he originated a new method in the study of finite groups, which is called "internal geometric analysis" by D. Gorenstein in his book: Finite Simple Groups, an Introduction to their Classification. In fact D. Gorenstein writes that this method can be regarded as second in importance for the classification of finite simple groups only to the local group-theoretic analysis created by J. Thompson
Member of
http://library.link/vocab/creatorName
Timmesfeld, Franz G
Dewey number
512.2
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
W4LojHc0uNY
Image bit depth
0
Language note
English
LC call number
QA174-183
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Monographs in Mathematics,
Series volume
95
http://library.link/vocab/subjectName
  • Group theory
  • Group Theory and Generalizations
Label
Abstract Root Subgroups and Simple Groups of Lie-Type, by Franz G. Timmesfeld, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
I Rank One Groups -- § 1 Definition, examples, basic properties -- § 2 On the structure of rank one groups -- § 3 Quadratic modules -- § 4 Rank one groups and buildings -- § 5 Structure and embeddings of special rank one groups -- II Abstract Root Subgroups -- § 1 Definitions and examples -- § 2 Basic properties of groups generated by abstract root subgroups -- § 3 Triangle groups -- §4 The radical R(G) -- § 5 Abstract root subgroups and Lie type groups -- III Classification Theory -- § 1 Abstract transvection groups -- § 2 The action of G on ? -- § 3 The linear groups and EK6 -- § 4 Moufang hexagons -- § 5 The orthogonal groups -- §6 D4(k) -- § 7 Metasymplectic spaces -- §8 E6(k),E7(k) and E8(k) -- § 9 The classification theorems -- IV Root involutions -- § 1 General properties of groups generated by root involutions -- § 2 Root subgroups -- § 3 The Root Structure Theorem -- § 4 The Rank Two Case -- V Applications -- § 1 Quadratic pairs -- § 2 Subgroups generated by root elements -- §3 Local BN-pairs -- References -- Symbol Index
Dimensions
unknown
Edition
1st ed. 2001.
Extent
1 online resource (XIII, 389 p.)
File format
multiple file formats
Form of item
online
Isbn
9783034875943
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-0348-7594-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000101331
  • (SSID)ssj0001295690
  • (PQKBManifestationID)11886408
  • (PQKBTitleCode)TC0001295690
  • (PQKBWorkID)11342747
  • (PQKB)11545304
  • (DE-He213)978-3-0348-7594-3
  • (MiAaPQ)EBC3085492
  • (EXLCZ)993400000000101331
Label
Abstract Root Subgroups and Simple Groups of Lie-Type, by Franz G. Timmesfeld, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Color
not applicable
Content category
text
Content type code
txt
Contents
I Rank One Groups -- § 1 Definition, examples, basic properties -- § 2 On the structure of rank one groups -- § 3 Quadratic modules -- § 4 Rank one groups and buildings -- § 5 Structure and embeddings of special rank one groups -- II Abstract Root Subgroups -- § 1 Definitions and examples -- § 2 Basic properties of groups generated by abstract root subgroups -- § 3 Triangle groups -- §4 The radical R(G) -- § 5 Abstract root subgroups and Lie type groups -- III Classification Theory -- § 1 Abstract transvection groups -- § 2 The action of G on ? -- § 3 The linear groups and EK6 -- § 4 Moufang hexagons -- § 5 The orthogonal groups -- §6 D4(k) -- § 7 Metasymplectic spaces -- §8 E6(k),E7(k) and E8(k) -- § 9 The classification theorems -- IV Root involutions -- § 1 General properties of groups generated by root involutions -- § 2 Root subgroups -- § 3 The Root Structure Theorem -- § 4 The Rank Two Case -- V Applications -- § 1 Quadratic pairs -- § 2 Subgroups generated by root elements -- §3 Local BN-pairs -- References -- Symbol Index
Dimensions
unknown
Edition
1st ed. 2001.
Extent
1 online resource (XIII, 389 p.)
File format
multiple file formats
Form of item
online
Isbn
9783034875943
Level of compression
uncompressed
Media category
computer
Media type code
c
Other control number
10.1007/978-3-0348-7594-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000101331
  • (SSID)ssj0001295690
  • (PQKBManifestationID)11886408
  • (PQKBTitleCode)TC0001295690
  • (PQKBWorkID)11342747
  • (PQKB)11545304
  • (DE-He213)978-3-0348-7594-3
  • (MiAaPQ)EBC3085492
  • (EXLCZ)993400000000101331

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