On Non-Generic Finite Subgroups of Exceptional Algebraic Groups ( Memoirs of the American Mathematical Society )

Publication series ： Memoirs of the American Mathematical Society

Author： Alastair J. Litterick  

Publisher： American Mathematical Society‎

Publication year： 2018

E-ISBN: 9781470444099

P-ISBN(Paperback): 9781470428372

Subject： O1 Mathematics

Keyword： 数学

Language： ENG

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On Non-Generic Finite Subgroups of Exceptional Algebraic Groups

Description

The study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.

Chapter

Cover

Title page

Chapter 1. Introduction and Results

Lie Primitivity

Complete Reducibility

Almost Simple Subgroups

Application: Finite Groups of Lie Type

Layout

Notation

Chapter 2. Background

2.1. Affine Algebraic Groups

2.2. Finite Subgroups

2.3. Subgroups of Positive Dimension

2.4. Representation Theory of Semisimple Groups

Chapter 3. Calculating and Utilising Feasible Characters

3.1. Feasible Characters

3.2. Deriving Theorem 2

3.3. Finding Fixed Vectors

3.4. Lie Imprimitivity of Subgroups in Theorem 1: Standard Cases

3.5. Postponed Cases of Theorem 1

Chapter 4. Normaliser Stability

4.1. Complete Reducibility and Normaliser Stability

4.2. Subspace Stabilisers and Normaliser Stability

4.3. Proof of Theorem 1: Standard Cases

4.4. Proof of Theorem 1: Special Cases

4.5. Proof of Theorem 8

Chapter 5. Complete Reducibility

5.1. Cohomology and Complements

5.2. Completely Reducible Subgroups

5.3. Proof of Theorem 4

Chapter 6. Tables of Feasible Characters

Notes on the Tables

6.1. 𝐹₄

6.2. 𝐸₆

6.3. 𝐸₇

6.4. 𝐸₈

Appendix A. Auxiliary Data

Bibliography

Back Cover

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