The Maximal Subgroups Of Positive Dimension In Exceptional Algebraic Groups
Download The Maximal Subgroups Of Positive Dimension In Exceptional Algebraic Groups full books in PDF, epub, and Kindle. Read online free The Maximal Subgroups Of Positive Dimension In Exceptional Algebraic Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : Martin W. Liebeck |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 242 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821834827 |
Intends to complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This title follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.
| Author | : Alastair J. Litterick |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 168 |
| Release | : 2018-05-29 |
| Genre | : Mathematics |
| ISBN | : 1470428377 |
The study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.
| Author | : Alexander Anatolievich Ivanov |
| Publisher | : World Scientific |
| Total Pages | : 347 |
| Release | : 2003-03-19 |
| Genre | : Mathematics |
| ISBN | : 9814486426 |
Over the past 20 years, the theory of groups — in particular simple groups, finite and algebraic — has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which there has been a major recent impetus provided by simple group theory. In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups.This important book contains 20 survey articles covering many of the above developments. It should prove invaluable for those working in the theory of groups and its applications.
| Author | : Martin W. Liebeck |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 2012-01-25 |
| Genre | : Mathematics |
| ISBN | : 0821869205 |
This 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. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.
| Author | : Gary M. Seitz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 205 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 0821825046 |
Let [italic]G be a simple algebraic group of exceptional type over an algebraically closed field of characteristic [italic]p. The subgroups of [italic]G maximal with respect to being closed and connected are determined, although mild restrictions on [italic]p are required in dealing with certain simple subgroups of low rank. For [italic]p = 0 we recover the results of Dynkin.
| Author | : David A. Craven |
| Publisher | : American Mathematical Society |
| Total Pages | : 226 |
| Release | : 2023-09-15 |
| Genre | : Mathematics |
| ISBN | : 147046702X |
| Author | : Ross Lawther |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 201 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821847694 |
Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.
| Author | : Adam R. Thomas |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 191 |
| Release | : 2021-06-18 |
| Genre | : Education |
| ISBN | : 1470443376 |
This paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.
| Author | : Alla Detinko |
| Publisher | : Springer |
| Total Pages | : 124 |
| Release | : 2013-01-13 |
| Genre | : Mathematics |
| ISBN | : 1447148142 |
Probabilistic Group Theory, Combinatorics and Computing is based on lecture courses held at the Fifth de Brún Workshop in Galway, Ireland in April 2011. Each course discusses computational and algorithmic aspects that have recently emerged at the interface of group theory and combinatorics, with a strong focus on probabilistic methods and results. The courses served as a forum for devising new strategic approaches and for discussing the main open problems to be solved in the further development of each area. The book represents a valuable resource for advanced lecture courses. Researchers at all levels are introduced to the main methods and the state-of-the-art, leading up to the very latest developments. One primary aim of the book’s approach and design is to enable postgraduate students to make immediate use of the material presented.
| Author | : Lino Di Martino |
| Publisher | : Birkhäuser |
| Total Pages | : 267 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 3034888198 |
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of finite characteristic, 3. buildings, and the geometry of projective and polar spaces, and 4. geometries of sporadic simple groups. We are grateful to the authors for their efforts in providing us with manuscripts in LaTeX. Barbara Priwitzer and Thomas Hintermann, Mathematics Editors of Birkhauser, have been very helpful and supportive throughout the preparation of this volume.
