The maximal subgroups of positive dimension in exceptional algebraic groups
Author(s)
Bibliographic Information
The maximal subgroups of positive dimension in exceptional algebraic groups
(Memoirs of the American Mathematical Society, no. 802)
American Mathematical Society, 2004
Available at 16 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"Volume 169, number 802 (third of 4 numbers)"
Includes bibliographical references (p. 225-227)
Description and Table of Contents
Description
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.
Table of Contents
Introduction Preliminaries Maximal subgroups of type $A_1$ Maximal subgroups of type $A_2$ Maximal subgroups of type $B_2$ Maximal subgroups of type $G_2$ Maximal subgroups $X$ with rank$(X)\geq3$ Proofs of Corollaries 2 and 3 Restrictions of small $G$-modules to maximal subgroups The tables for Theorem 1 and Corollary 2 Appendix: $E_8$ structure constants References.
by "Nielsen BookData"