Irreducible Geometric Subgroups Of Classical Algebraic Groups

Author : Timothy C. Burness,
Publisher : American Mathematical Soc.
ISBN 13 : 1470414945
Total Pages : 100 pages
Book Rating : 4.48/5 ( download)

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Download or read book Irreducible Geometric Subgroups of Classical Algebraic Groups written by Timothy C. Burness, and published by American Mathematical Soc.. This book was released on 2016-01-25 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .

Author : Timothy C. Burness
Publisher : American Mathematical Soc.
ISBN 13 : 147041046X
Total Pages : 122 pages
Book Rating : 4.69/5 ( download)

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Download or read book Irreducible Almost Simple Subgroups of Classical Algebraic Groups written by Timothy C. Burness and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Gary M. Seitz
Publisher : American Mathematical Soc.
ISBN 13 : 0821824279
Total Pages : 294 pages
Book Rating : 4.76/5 ( download)

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Download or read book The Maximal Subgroups of Classical Algebraic Groups written by Gary M. Seitz and published by American Mathematical Soc.. This book was released on 1987 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [italic]V be a finite dimensional vector space over an algebraically closed field of characteristic p [greater than] 0 and let G = SL([italic]V), Sp([italic]V), or SO([italic]V). The main result describes all closed, connected, overgroups of [italic]X in SL([italic]V), assuming [italic]X is a closed, connected, irreducible subgroup of G.

Author : Donna M. Testerman
Publisher : American Mathematical Soc.
ISBN 13 : 0821824538
Total Pages : 198 pages
Book Rating : 4.35/5 ( download)

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Download or read book Irreducible Subgroups of Exceptional Algebraic Groups written by Donna M. Testerman and published by American Mathematical Soc.. This book was released on 1988 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Meinolf Geck
Publisher : Clarendon Press
ISBN 13 : 0191663727
Total Pages : 320 pages
Book Rating : 4.27/5 ( download)

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Download or read book An Introduction to Algebraic Geometry and Algebraic Groups written by Meinolf Geck and published by Clarendon Press. This book was released on 2013-03-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.

Author : Larry C. Grove
Publisher : American Mathematical Soc.
ISBN 13 : 0821820192
Total Pages : 181 pages
Book Rating : 4.93/5 ( download)

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Download or read book Classical Groups and Geometric Algebra written by Larry C. Grove and published by American Mathematical Soc.. This book was released on 2002 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level text on the classical groups: groups of matrices, or (more often) quotients of matrix groups by small normal subgroups. It pulls together into a single source the basic facts about classical groups defined over fields, together with the required geometrical background information, from first principles. The chief prerequisites are basic linear algebra and abstract algebra, including fundamentals of group theory and some Galois Theory. The author teaches at the U. of Arizona. c. Book News Inc.

Author : Peter B. Kleidman
Publisher : Cambridge University Press
ISBN 13 : 052135949X
Total Pages : 317 pages
Book Rating : 4.98/5 ( download)

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Download or read book The Subgroup Structure of the Finite Classical Groups written by Peter B. Kleidman and published by Cambridge University Press. This book was released on 1990-04-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Alexander Anatolievich Ivanov
Publisher : World Scientific
ISBN 13 : 9814486426
Total Pages : 347 pages
Book Rating : 4.22/5 ( download)

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Download or read book Groups, Combinatorics And Geometry written by Alexander Anatolievich Ivanov and published by World Scientific. This book was released on 2003-03-19 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Cambridge University Press
ISBN 13 : 0521406854
Total Pages : 505 pages
Book Rating : 4.57/5 ( download)

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Download or read book Groups, Combinatorics and Geometry written by Martin W. Liebeck and published by Cambridge University Press. This book was released on 1992-09-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers on the subject of the classification of finite simple groups.

Author : U. Meierfrankenfeld
Publisher : American Mathematical Soc.
ISBN 13 : 1470418770
Total Pages : 356 pages
Book Rating : 4.79/5 ( download)

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Download or read book The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup written by U. Meierfrankenfeld and published by American Mathematical Soc.. This book was released on 2016-06-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.