The Irreducible Subgroups Of Exceptional Algebraic Groups

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The Irreducible Subgroups Of Exceptional Algebraic Groups

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Author : Adam R. Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18

The Irreducible Subgroups Of Exceptional Algebraic Groups written by Adam R. Thomas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.

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.

Irreducible Subgroups Of Exceptional Algebraic Groups

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Author : Donna M. Testerman
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

Irreducible Subgroups Of Exceptional Algebraic Groups written by Donna M. Testerman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

Let [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on some rational [italic]k[italic]Y module [italic]V. This extends work of Dynkin who obtained a similar classification for algebraically closed fields of characteristic 0. The main result has been combined with work of G. Seitz to obtain a classification of the maximal closed connected subgroups of the classical algebraic groups defined over [italic]k.

On Non Generic Finite Subgroups Of Exceptional Algebraic Groups

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Author : Alastair J. Litterick
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29

On Non Generic Finite Subgroups Of Exceptional Algebraic Groups written by Alastair J. Litterick and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Mathematics categories.

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.

Irreducible Subgroups Of Exceptional Algebraic Groups

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Author : Adam Robert Thomas
language : en
Publisher:
Release Date : 2014

Irreducible Subgroups Of Exceptional Algebraic Groups written by Adam Robert Thomas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

Maximal Subgroups Of Exceptional Algebraic Groups

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Author : Gary M. Seitz
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Maximal Subgroups Of Exceptional Algebraic Groups written by Gary M. Seitz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

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.

Irreducible Geometric Subgroups Of Classical Algebraic Groups

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Author : Timothy C. Burness,
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25

Irreducible Geometric Subgroups Of Classical Algebraic Groups written by Timothy C. Burness, and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-25 with Mathematics categories.

Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .

The Maximal Subgroups Of Positive Dimension In Exceptional Algebraic Groups

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Author : Martin W. Liebeck
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

The Maximal Subgroups Of Positive Dimension In Exceptional Algebraic Groups written by Martin W. Liebeck and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

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.

Groups St Andrews 2017 In Birmingham

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Author : C. M. Campbell
language : en
Publisher: Cambridge University Press
Release Date : 2019-04-11

Groups St Andrews 2017 In Birmingham written by C. M. Campbell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-11 with Mathematics categories.

These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.

Finite And Locally Finite Groups

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Author : B. Hartley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finite And Locally Finite Groups written by B. Hartley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni

Groups And Geometries

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Author : Lino Di Martino
language : en
Publisher: Springer Science & Business Media
Release Date : 1998

Groups And Geometries written by Lino Di Martino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

The Conference on Groups and Geometries held in Siena in 1996, addressed 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. Algebraists and geometers will encounter in this conference record a stimulating collection of ideas stemming from work in such areas as 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.