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Abstract Root Subgroups and Simple Groups of Lie-Type

Author: Franz Georg Timmesfeld
Publisher: Basel : Birkhäuser Basel, 2001.
Series: Monographs in mathematics, 95.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The present book is the first to systematically treat the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Fischer and the author. It was extended to arbitrary groups in the 1990s by the author. The theory of abstract root subgroups is an important  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Franz Georg Timmesfeld
ISBN: 9783034875943 3034875940
OCLC Number: 851785998
Description: 1 online resource (xiii, 389 pages).
Contents: I Rank One Groups --
ʹ 1 Definition, examples, basic properties --
ʹ 2 On the structure of rank one groups --
ʹ 3 Quadratic modules --
ʹ 4 Rank one groups and buildings --
ʹ 5 Structure and embeddings of special rank one groups --
II Abstract Root Subgroups --
ʹ 1 Definitions and examples --
ʹ 2 Basic properties of groups generated by abstract root subgroups --
ʹ 3 Triangle groups --
ʹ4 The radical R(G) --
ʹ 5 Abstract root subgroups and Lie type groups --
III Classification Theory --
ʹ 1 Abstract transvection groups --
ʹ 2 The action of G on? --
ʹ 3 The linear groups and EK6 --
ʹ 4 Moufang hexagons --
ʹ 5 The orthogonal groups --
ʹ6 D4(k) --
ʹ 7 Metasymplectic spaces --
ʹ8 E6(k), E7(k) and E8(k) --
ʹ 9 The classification theorems --
IV Root involutions --
ʹ 1 General properties of groups generated by root involutions --
ʹ 2 Root subgroups --
ʹ 3 The Root Structure Theorem --
ʹ 4 The Rank Two Case --
V Applications --
ʹ 1 Quadratic pairs --
ʹ 2 Subgroups generated by root elements --
ʹ3 Local BN-pairs --
References --
Symbol Index.
Series Title: Monographs in mathematics, 95.
Responsibility: by Franz Georg Timmesfeld.

Abstract:

This book systematically treats the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. The theory of abstract root  Read more...

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"The book is well written: the style is concise but not hard and most of the book is not too difficult to read for a graduate student. Some parts of it are certainly suited for a Read more...

 
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