Linear Algebraic Groups and Finite Groups of Lie Type

Gunter Malle, Donna Testerman

• Publisher: Cambridge University Press
• Year: 2011
• Print ISBN: 9781107008540
• eBook ISBN: 9781139120036
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.

Table of contents

• Cover
• Title
• Copyright
• Contents
• Preface
• Tables
• Notation
• PART I LINEAR ALGEBRAIC GROUPS
• PART II SUBGROUP STRUCTURE AND REPRESENTATION THEORY OF SEMISIMPLE ALGEBRAIC GROUPS
• PART III FINITE GROUPS OF LIE TYPE
• Appendix A Root systems
• Appendix B Subsystems
• Appendix C Automorphisms of root systems
• References
• Index