Last edited by Gam
Friday, May 8, 2020 | History

5 edition of Abstract Root Subgroups & Simple Groups of Lie-Type (Monographs in Mathematics) found in the catalog.

# Abstract Root Subgroups & Simple Groups of Lie-Type (Monographs in Mathematics)

## by Franz G. Timmesfeld

Written in English

Subjects:
• Groups & group theory,
• Science/Mathematics,
• Lie Groups,
• Linear Algebra,
• Mathematics,
• Algebra - Linear,
• General,
• Group Theory,
• Mathematics / Group Theory,
• buildings and generalized polygons

• The Physical Object
FormatHardcover
Number of Pages400
ID Numbers
Open LibraryOL9826358M
ISBN 103764365323
ISBN 109783764365325

Learn the definition of a subgroup. If you ’d like to help us make videos more quickly, you can support us on Patreon at https://www. The definition of "almost simple" implicitly used in the question (as clarified by Geoff and Nick) is convenient for the study of finite simple groups but is somewhat restrictive in requiring the given group to contain a normal simple subgroup and be included in its automorphism group.

Special Moufang sets (or more precisely special abstract rank one groups) were given a considerable amount of attention in Timmesfelds book (Abstract Root Subgroups and Simple Groups of Lie-Type). I will discuss, and give partial results on the conjecture that says that a special Moufang set has abelian root groups. Tee/Kaffee/Gebäck ab Uhr.   Normal Subgroups and Quotient Groups (aka Factor Groups) - Abstract Algebra - Duration: Direct Products of Groups (Abstract Algebra) - Duration: Socratica , views.

Subspace stabilizers and maximal subgroups of exceptional groups of Lie type David A. Craven June 7, Abstract In , Liebeck and Seitz introduced a constant t(G), dependent on the root system of a reductive algebraic group G and proved that if x is a semisimple File Size: KB. If you have a disability and are having trouble accessing information on this website or need materials in an alternate format, contact [email protected] for [email protected] for Cited by: 4.

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### Abstract Root Subgroups & Simple Groups of Lie-Type (Monographs in Mathematics) by Franz G. Timmesfeld Download PDF EPUB FB2

The theory of abstract root subgroups is an important tool to study and classify simple classical and Lie-type groups. Read more Read less The Amazon Book ReviewAuthor: Franz G. Timmesfeld. Abstract Root Subgroups and Simple Groups of Lie-Type. Usually dispatched within 3 to 5 business days.

Usually dispatched within 3 to 5 business days. It was already in [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G.

It was already in [Fis66] when B. Fischer raised the question: Which finite groups can be generated by a conjugacy class D of involutions, the product of any two of which has order 1, 2 or 37 Such a class D he called a class of 3-tmnspositions of G. Abstract Root Subgroups and Simple Groups of Lie-Type.

[Franz Georg Timmesfeld] -- The present book is the first to systematically treat the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups.

Book review: Abstract Root Subgroups and Simple Groups of Lie-Type: Published in: Nieuw Archief voor Wiskunde, 5/6, - ISSN Author: Cohen, A.M.

Publisher: Discrete Algebra and Geometry, Research on miscellaneous topics in mathematics, not included in one of the research schools: Date issued: Access: Restricted Access Author: A.M.

Cohen. Finally in §5 we show that each simple group of Lie type (in a general sense) is generated by a class of abstract root subgroups.

The results of this chapter are, if not mentioned otherwise, from [Tim90a], [Tim91], [Tim99] or [Tim00b].Author: Franz Georg Timmesfeld. Let K be a field and G a quasi-simple subgroup of the Chevalley group F 4 (K).

We assume that G is generated by a class Σ of abstract root subgroups such that there are A, C ∈ Σ with [ A, C ]∈ Σ and any A ∈ Σ is contained in a long root subgroup of F 4 (K).Cited by: 4.

Maximal subgroups of exceptional algebraic groups Let G be a simple algebraic group of exceptional type, deﬁned over an algebraically closed ﬁeld k of characteristic p ≥ 0. Let M ⊂ G be a maximal positive-dimensional closed subgroup.

By the Borel-Tits theorem, if M is not reductive, then M is a maximal parabolic subgroup of G. Example 2: Any group has at least 2 subgroups; itself and the trivial group {}. These are called the improper and trivial subgroups of G {\displaystyle G}, respectively.

Naturally, we would like to have a method of determining whether a given subset of a group is a subgroup. In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite phrase group of Lie type does not have a widely accepted precise definition, but the important collection of finite simple groups of Lie type does have a.

Abstract root subgroups and simple groups of Lie-type. [Franz Georg Timmesfeld] -- "This book is of interest to mathematicians working in different areas such as finite group theory, classical groups, algebraic and Lie-type groups, buildings and generalized polygons.

Abstract: In this paper we examine embeddings of alternating groups and symmetric groups into almost simple groups of exceptional type. In particular, we prove that unless the alternating or symmetric group has degree 6 or 7, there is no maximal subgroup of any almost simple group with socle an exceptional group of Lie type that is an alternating or symmetric group.

Abstract Both Timmesfeld's abstract root subgroups and simple Lie algebras generated by extremal elements lead to root filtration spaces: synthetically defined geometries on points and lines which can be characterized as root shadow spaces of by: Pacific J. Math. VolumeNumber 1 (), The root subgroups for maximal tori in finite groups of Lie type.

Gary M. SeitzCited by: II Abstract Root Subgroups.- 1 Definitions and examples.- 2 Basic properties of groups generated by abstract root subgroups.- 3 Triangle groups.- 4 The radical R(G).- 5 Abstract root subgroups and.

The list of finite simple groups of Lie type has been understood for half a century, modulo some differences in notation (and identifications between some of the very small groups coming from different Lie types). Call this collection of isomorphism classes of finite groups $\mathcal{S}$.

But it's not clear to me that there is a similar consensus about the meaning of "finite group of Lie type". An equivalent definition of a simple Lie group follows from the Lie correspondence: a connected Lie group is simple if its Lie algebra is a simple.

An important technical point is that a simple Lie group may contain discrete normal subgroups, hence being a simple Lie group is different from being simple as an abstract group. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. We study finite subgroups of exceptional groups of Lie type, in particular maximal subgroups.

Reduction theorems allow us to concentrate on almost simple subgroups, the main case being those with socle X(q) ofLie type in the natural characteristic. Our approach is to show that for sufficiently large q. Martin W. Liebeck and Gary M. Seitz, Subgroups generated by root elements in groups of Lie type, Ann.

of Math. (2) (), no. 2, – MR/Author: Michael Aschbacher. This book offers a single source of basic facts about the structure of the finite simple groups with emphasis on a detailed description of their local subgroup structures, coverings and automorphisms.

The method is by examination of the specific groups, rather than by the development of an abstract theory of simple groups.

LetG be a Chevalley group over the fieldk and the class of long root subgroups ofG or an abstract group generated by a class of k-root subgroups.

Then elements ofA, A are called root-elements.The book describes the finite simple groups in three parts: alternating groups, groups of Lie type and sporadics. While this is a useful reference for some results (lists of maximal subgroups, etc.), the explanations are not easy to follow, and I did not feel that I gained any insight into the subject of the by: However, groups of Lie type are usually described using the concept of root subgroups and the Chevalley commutator formula.

Other than (a) which linear combination of simple roots are still roots, and (b) the constants appearing in the commutator formula, the description is identical for all groups of Lie type.