Irreducible Almost Simple Subgroups Of Classical Algebraic Groups
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Irreducible Almost Simple Subgroups Of Classical Algebraic Groups
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Author : Timothy C. Burness
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26
Irreducible Almost Simple 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 2015-06-26 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 nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.
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 Subgroup Structure Of The Finite Classical Groups
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Author : Peter B. Kleidman
language : en
Publisher: Cambridge University Press
Release Date : 1990-04-26
The Subgroup Structure Of The Finite Classical Groups written by Peter B. Kleidman 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 1990-04-26 with Mathematics categories.
With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.
Discrete Subgroups Of Semisimple Lie Groups
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Author : Gregori A. Margulis
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-02-15
Discrete Subgroups Of Semisimple Lie Groups written by Gregori A. Margulis 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 1991-02-15 with Mathematics categories.
Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students.
Linear Algebraic Groups And Finite Groups Of Lie Type
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Author : Gunter Malle
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Linear Algebraic Groups And Finite Groups Of Lie Type written by Gunter Malle 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 2011-09-08 with Mathematics categories.
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
The Local Structure Theorem For Finite Groups With A Large P Subgroup
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Author : U. Meierfrankenfeld
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-21
The Local Structure Theorem For Finite Groups With A Large P Subgroup written by U. Meierfrankenfeld 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 2016-06-21 with Mathematics categories.
Let p be a prime, G a finite Kp-group S a Sylow p-subgroup of G and Q a large subgroup of G in S (i.e., CG(Q)≤Q and NG(U)≤NG(Q) for 1≠U≤CG(Q)). Let L be any subgroup of G with S≤L, Op(L)≠1 and Q⋬L. In this paper the authors determine the action of L on the largest elementary abelian normal p-reduced p-subgroup YL of L.
Algebraic Groups And Their Representations
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Author : R.W. Carter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Groups And Their Representations written by R.W. Carter 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 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.
Algebraic Groups
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Author : J. S. Milne
language : en
Publisher: Cambridge University Press
Release Date : 2017-09-21
Algebraic Groups written by J. S. Milne 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 2017-09-21 with Mathematics categories.
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Nil Bohr Sets And Almost Automorphy Of Higher Order
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Author : Wen Huang
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-26
Nil Bohr Sets And Almost Automorphy Of Higher Order written by Wen Huang 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 2016-04-26 with Mathematics categories.
Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d∈N does the collection of {n∈Z:S∩(S−n)∩…∩(S−dn)≠∅} with S syndetic coincide with that of Nild Bohr0 -sets? In the second part, the notion of d -step almost automorphic systems with d∈N∪{∞} is introduced and investigated, which is the generalization of the classical almost automorphic ones.
Classification Of E 0 Semigroups By Product Systems
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Author : Michael Skeide
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-10
Classification Of E 0 Semigroups By Product Systems written by Michael Skeide 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 2016-03-10 with Mathematics categories.
In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.