Ebook: 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.

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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.

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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.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-19
Preliminaries....Pages 21-51
The Structure of SL2(q) and its Modules....Pages 53-66
Elementary Properties of Symplectic Amalgams....Pages 67-80
The Structure of Q?....Pages 81-92
Reduced Symplectic Amalgams....Pages 93-112
The Components of L?/Q?....Pages 113-123
The Story so Far....Pages 125-140
Groups of Lie Type....Pages 141-162
Modules for Groups of Lie Type....Pages 163-176
Sporadic Simple Groups and Their Modules....Pages 177-186
Alternating Groups and Their Modules....Pages 187-188
Rank One Groups....Pages 189-213
Lie Type Groups in Characteristic p and Rank ? 2....Pages 215-247
Lie Type Groups and Natural Modules....Pages 249-255
Alternating Groups....Pages 257-264
Sporadic Simple Groups....Pages 265-270
The Proof of the Main Theorems....Pages 271-291
A Brief Survey of Amalgam Results....Pages 293-311
Back Matter....Pages 313-314
....Pages 315-323