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The Resource Abstract Root Subgroups and Simple Groups of LieType, by Franz G. Timmesfeld, (electronic resource)
Abstract Root Subgroups and Simple Groups of LieType, by Franz G. Timmesfeld, (electronic resource)
Resource Information
The item Abstract Root Subgroups and Simple Groups of LieType, by Franz G. Timmesfeld, (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 Abstract Root Subgroups and Simple Groups of LieType, by Franz G. Timmesfeld, (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
 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 3tmnspositions 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 3cycle (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 3transpositions, 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 grouptheoretic analysis created by J. Thompson
 Language

 eng
 eng
 Edition
 1st ed. 2001.
 Extent
 1 online resource (XIII, 389 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 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 BNpairs
 References
 Symbol Index
 Isbn
 9783034875943
 Label
 Abstract Root Subgroups and Simple Groups of LieType
 Title
 Abstract Root Subgroups and Simple Groups of LieType
 Statement of responsibility
 by Franz G. Timmesfeld
 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 3tmnspositions 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 3cycle (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 3transpositions, 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 grouptheoretic analysis created by J. Thompson
 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
 QA174183
 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 LieType, by Franz G. Timmesfeld, (electronic resource)
 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 BNpairs  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
 10.1007/9783034875943
 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
 (DEHe213)9783034875943
 (MiAaPQ)EBC3085492
 (EXLCZ)993400000000101331
 Label
 Abstract Root Subgroups and Simple Groups of LieType, by Franz G. Timmesfeld, (electronic resource)
 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 BNpairs  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
 10.1007/9783034875943
 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
 (DEHe213)9783034875943
 (MiAaPQ)EBC3085492
 (EXLCZ)993400000000101331
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