The Maximal Subgroups of Positive Dimension in Exceptional Algebraic Groups
- ISBN-10
- 0821834827
- ISBN-13
- 9780821834824
- Category
- Mathematics
- Pages
- 227
- Language
- English
- Published
- 2004
- Publisher
- American Mathematical Soc.
- Authors
- Martin W. Liebeck, Gary M. Seitz
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.
Get the book
Other editions
-
- 2004-03-19
- 227 pages
- Paperback
- American Mathematical Soc.
Similar books
-
The Irreducible Subgroups of Exceptional Algebraic Groups
By Adam R. Thomas1, 261–297, DOI 10.1016/S0021-8693(02)00649-X. Special issue celebrating the 80th birthday of Robert Steinberg. MR1973585 M. W. Liebeck and G. M. Seitz, The maximal subgroups of positive dimension in exceptional algebraic groups, Mem.
-
Maximal $textrm {PSL}_2$ Subgroups of Exceptional Groups of Lie Type
By David A. CravenMR1351124 R. Lawther, Unipotent classes in maximal subgroups of exceptional algebraic groups, J. Algebra 322 (2009), no. ... MR1717629 M. W. Liebeck and G. M. Seitz, The maximal subgroups of positive dimension in exceptional algebraic ...
-
Maximal Subgroups of Exceptional Algebraic Groups
By Gary M. Seitz... with respect to being closed and connected and which contain a nontrivial element of a long root subgroup. ... Our approach is to study the action of X on L(G), the Lie algebra of G. In §2 we make several reductions under the ...
-
On Non-Generic Finite Subgroups of Exceptional Algebraic Groups
By Alastair J. LitterickMR1367085 [53] M. W. Liebeck and G. M. Seitz, Maximal subgroups of exceptional groups of Lie type, ... MR1717629 [58] M. W. Liebeck and G. M. Seitz, The maximal subgroups of positive dimension in ex- ceptional algebraic groups, Mem.
-
Linear Algebraic Groups and Finite Groups of Lie Type
By Gunter Malle, Donna TestermanThen one of the following holds: (2) (1) M is a parabolic subgroup, M is the normalizer of some connected reductive ... An elementary abelian r-subgroup R of G, with r = char(k), is called a Jordan subgroup of G if it satisfies the ...
-
Groups Combinatorics & Geometry: Durham 2001
By Martin W. Liebeck, A. A. Ivanov, J. SaxlOver the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics.
-
Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras
By Martin W. Liebeck, Gary M. SeitzThis book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras.
-
Groups St Andrews 2017 in Birmingham
By C. M. Campbell, E. F. Robertson, M. R. Quick[11] B. Ford, Overgroups of irreducible linear groups, I, J. Algebra 181 (1996), 26–69. ... [19] M.W. Liebeck and G.M. Seitz, The maximal subgroups of positive dimension in exceptional algebraic groups, Mem. Amer. Math. Soc. 802, 2004.
-
Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
By Donna M. Testerman, Ross LawtherRoss Lawther, Donna M. Testerman ... collection of T-weights on V is the union (with multiplicities) of the sets {d – 1, d – 3, . . . , 3– d, 1 – d}, where the union runs over the Jordan blocks of e on V and d is the size of the block ...
-
Groups and Geometries: Siena Conference, September 1996
By Lino Di Martino, William Kantor, Guglielmo LunardonTrends in Mathematics, (C) 1998 Birkhäuser Verlag Basel/Switzerland Maximal Subgroups of Finite Exceptional Groups Gary M. ... Let G be a simple adjoint algebraic group of exceptional type over an algebraically closed field of positive ...