Overview

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 tool to study and classify simple classical and Lie-type groups. It is strongly related to the theory of root groups on buildings developed by J. Tits, which in turn extends the theory of root subgroups of Chevalley groups. The book is of interest to mathematicians working in different areas such as finite group theory, classical groups, algebraic and Lie-type groups, buildings and generalized polygons. It will also be welcomed by the graduate student in any of the above subjects, as well as the researcher working in any of these areas. Parts of it can also be used for graduate classes. Large parts of the book are self-contained and accessible with reasonable knowledge in abstract group theory and classical groups. Its main purpose is to give complete and partially new proofs of results that are quite unaccessible in the literature.

Full Product Details

Author:   Franz G. Timmesfeld
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2001 ed.
Volume:   95
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   1.650kg
ISBN:  

9783764365325

ISBN 10:   3764365323
Pages:   389
Publication Date:   01 August 2001
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of 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.

Reviews

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 class. --Mathematical Reviews

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 class. --Mathematical Reviews

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 class. --Mathematical Reviews

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 class. <p>--Mathematical Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions