Symplectic Amalgams

Springer monographs in mathematics

Peter Rowley, Christopher Parker

362 pages, parution le 08/07/2002

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Résumé

The latter half of the twentieth century saw dramatic advances in group theory, particularly in finite group theory. During this time, the amalgam method emerged as the most powerful and promising tool and is playing a central role in the revision of the classification of finite simple groups. In this book, the authors chart the rise of the "amalgam method" and aim to classify symplectic amalgams with the intention of providing a complete overview of research in the field that will be accessible to both specialists and non-specialists alike. The aim of this book is the classification of symplectic amalgams - structures which are intimately related to the finite simple groups. In all there sixteen infinite families of symplectic amalgams together with 62 more exotic examples. The classification touches on many important aspects of modern group theory: - p-local analysis - the amalgam method - representation theory over finite fields; and - properties of the finite simple groups. The account is for the most part self-contained and the wealth of detail makes this book an excellent introduction to these recent developments for graduate students, as well as a valuable resource and reference for specialists in the area.

Contents

1. Introduction
2. Preliminaries
3. The Structure of SL2 ( q ) and its Modules
4. Elementary Properties of Symplectic Amalgams
5. The Structure of Qa
6. The Lb-Chief Factors in Vb
7. Reduced Symplectic Amalgams
8. The Largest Normal pSubgroup of Lb/Qb
9. The Components of Lb/Qb
10. The Reduction to Quasisimple when CUa (Ua / Za) Qb
11. A First Look at the Amalgams with oe Vb / Z (Vb) oe = q4
12. The Story so Far
13. Groups of Lie-Type
14. Modules for Groups of Lie Type
15. Sporadic Simple Groups and their Modules
16. Alternating Groups and their Modules
17. Rank One Groups
18. Lie-Type Groups in Characteristic p and Rank 2
19. Lie-Type Groups and Natural Modules
20. Lie Type Groups in Characteristic not p
21. Alternating Groups
22. Sporadic Simple Groups
23. The Proof of the Main Theorems
Index.

L'auteur - Peter Rowley

Peter Rowley is Professor of Mathematics at UMIST, Manchester, UK.

L'auteur - Christopher Parker

Christopher Parker is a Senior Lecturer in Mathematics at the University of Birmingham, UK

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Peter Rowley, Christopher Parker
Parution	08/07/2002
Nb. de pages	362
Format	16 x 24
Couverture	Relié
Poids	708g
Intérieur	Noir et Blanc
EAN13	9781852334307
ISBN13	978-1-85233-430-7