Symplectic Amalgams

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.

Contenu

Introduction Preliminaries The Structure of SL2 ( q ) and its Modules Elementary Properties of Symplectic Amalgams The Structure of Qa The Lb-Chief Factors in Vb Reduced Symplectic Amalgams The Largest Normal p'-Subgroup of Lb/Qb The Components of Lb/Qb The Reduction to Quasisimple when CUa (Ua / Za) Qb A First Look at the Amalgams with ö Vb / Z (Vb) ö =3D q4 The Story so Far Groups of Lie-Type Modules for Groups of Lie Type Sporadic Simple Groups and their Modules Alternating Groups and their Modules Rank One Groups Lie-Type Groups in Characteristic p and Rank 2 Lie-Type Groups and Natural Modules Lie Type Groups in Characteristic not p Alternating Groups Sporadic Simple Groups The Proof of the Main Theorems A Brief Survey of Amalgam Results References Index