# Simple groups of Lie type

@inproceedings{MacDonald1972SimpleGO, title={Simple groups of Lie type}, author={Ian G. MacDonald}, year={1972} }

Partial table of contents: The Classical Simple Groups. Weyl Groups. Simple Lie Algebras. The Chevalley Groups. Unipotent Subgroups. The Diagonal and Monomial Subgroups. The Bruhat Decomposition. Polynomial Invariants of the Weyl Group. The Exponents of the Weyl Group. Further Properties of the Chevalley Groups. Generators, Relations and Automorphisms in Chevalley Groups. The Twisted Simple Groups. Further Properties of the Twisted Groups. Associated Geometrical Structures. Sporadic Simple…

## 1,818 Citations

### CONSTRUCTING MAXIMAL SUBGROUPS OF CLASSICAL GROUPS

- Mathematics
- 2005

The maximal subgroups of the finite classical groups are divided by a theorem of Aschbacher into nine classes. In this paper, the authors show how to construct those maximal subgroups of the finite…

### Classical groups and generalized simple groups of Lie type

- MathematicsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- 1989

Abstract In this note, for any given simple group obtained from an orthogonal or unitary group of non-zero index, by a procedure similar to the construction of Chevalley groups and twisted groups, we…

### On the chief factors of maximal parabolic subgroups of twisted classical groups

- Mathematics
- 2015

For the finite simple groups of twisted Lie types 2Al and 2Dl, we specify the description for the chief factors of a maximal parabolic subgroup which are involved in its unipotent radical. We prove a…

### Permutation Groups with a Cyclic Two-Orbits Subgroup and Monodromy Groups of Laurent Polynomials

- Mathematics
- 2011

We classify the nite primitive permutation groups which have a cyclic subgroup with two orbits. This extends classical topics in permutation group theory, and has arithmetic consequences. By a…

### Permutation Groups with a Cyclic Two-Orbits Subgroup and Monodromy Groups of Siegel Functions

- Mathematics
- 2001

We classify the finite primitive permutation groups which have a cyclic subgroup with two orbits. This extends classical topics in permutation group theory, and has arithmetic consequences. By a…

### Permutation Groups with a Cyclic Two-Orbits Subgroup and Monodromy Groups of Siegel Functions

- Mathematics
- 2002

We classify the finite primitive permutation groups which have a cyclic subgroup with two orbits. This extends classical topics in permutation group theory, and has arithmetic consequences. By a…

### The P-radical classes in simple algebraic groups and finite groups of Lie type

- Mathematics
- 2012

Abstract. Given either a simple algebraic group or a finite group of Lie type, of rank at least 2, and a maximal parabolic subgroup, we determine which non-trivial unipotent classes have the property…

### On the simple groups of Suzuki and Ree

- Mathematics
- 2013

We develop a new and uniform approach to the three families of twisted simple groups of Lie type discovered by Suzuki and Ree, without using Lie algebras. A novel type of algebraic structure is…

### The normal structure of the unipotent subgroup in Lie type groups and its extremal subgroups

- Mathematics
- 2012

We study the normal structure of the unipotent radical U of a Borel subgroup in a Lie type group over a field K. Thus, all maximal Abelian normal subgroups in U are described. This gives a new…

### The normal structure of the unipotent subgroup in Lie type groups and its extremal subgroups

- MathematicsJournal of Mathematical Sciences
- 2012

We study the normal structure of the unipotent radical U of a Borel subgroup in a Lie type group over a field K. Thus, all maximal Abelian normal subgroups in U are described. This gives a new…