| 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 |
| 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 169; 2004; 227 ppMSC: 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.
ReadershipGraduate students and research mathematicians interested in group theory and generalizations.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries
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3. Maximal subgroups of type $A_1$
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4. Maximal subgroups of type $A_2$
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5. Maximal subgroups of type $B_2$
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6. Maximal subgroups of type $G_2$
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7. Maximal subgroups $X$ with $\operatorname {rank}(X) \geq 3$
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8. Proofs of Corollaries 2 and 3
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9. Restrictions of small $G$-modules to maximal subgroups
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10. The tables for Theorem 1 and Corollary 2
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11. Appendix: $E_8$ structure constants
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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.
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 $\operatorname {rank}(X) \geq 3$
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8. Proofs of Corollaries 2 and 3
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9. Restrictions of small $G$-modules to maximal subgroups
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10. The tables for Theorem 1 and Corollary 2
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11. Appendix: $E_8$ structure constants
