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The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups
 
Martin W. Liebeck Imperial College, London, UK
Gary M. Seitz University of Oregon, Eugene, OR
The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups
eBook ISBN:  978-1-4704-0400-0
Product Code:  MEMO/169/802.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $47.40
The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups
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The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups
Martin W. Liebeck Imperial College, London, UK
Gary M. Seitz University of Oregon, Eugene, OR
eBook ISBN:  978-1-4704-0400-0
Product Code:  MEMO/169/802.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $47.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1692004; 227 pp
    MSC: Primary 20;

    In this paper we complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.

    A number of consequences are obtained. It follows from the main theorem that a simple algebraic group over an algebraically closed field has only finitely many conjugacy classes of maximal subgroups of positive dimension. It also follows that the maximal subgroups of sufficiently large order in finite exceptional groups of Lie type are known.

    Readership

    Graduate students and research mathematicians interested in group theory and generalizations.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Preliminaries
    • 3. Maximal subgroups of type $A_1$
    • 4. Maximal subgroups of type $A_2$
    • 5. Maximal subgroups of type $B_2$
    • 6. Maximal subgroups of type $G_2$
    • 7. Maximal subgroups $X$ with $\operatorname {rank}(X) \geq 3$
    • 8. Proofs of Corollaries 2 and 3
    • 9. Restrictions of small $G$-modules to maximal subgroups
    • 10. The tables for Theorem 1 and Corollary 2
    • 11. Appendix: $E_8$ structure constants
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1692004; 227 pp
MSC: Primary 20;

In this paper we complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.

A number of consequences are obtained. It follows from the main theorem that a simple algebraic group over an algebraically closed field has only finitely many conjugacy classes of maximal subgroups of positive dimension. It also follows that the maximal subgroups of sufficiently large order in finite exceptional groups of Lie type are known.

Readership

Graduate students and research mathematicians interested in group theory and generalizations.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries
  • 3. Maximal subgroups of type $A_1$
  • 4. Maximal subgroups of type $A_2$
  • 5. Maximal subgroups of type $B_2$
  • 6. Maximal subgroups of type $G_2$
  • 7. Maximal subgroups $X$ with $\operatorname {rank}(X) \geq 3$
  • 8. Proofs of Corollaries 2 and 3
  • 9. Restrictions of small $G$-modules to maximal subgroups
  • 10. The tables for Theorem 1 and Corollary 2
  • 11. Appendix: $E_8$ structure constants
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.