Author: A. S. DetinkoPublisher:
ISBN:
Category :
Languages : en
Pages : 17
Book Description
Classification of Irreducible Maximal Solvable Subgroups of Prime Degree Classical Groups Over Finite Field. A New GAP Group Library for Irreducible Maximal Solvable Subgroups of Prime Degree Classical Groups. Deciding Finiteness for Matrix Groups Over
Author: A. S. DetinkoMaximal Solvable Subgroups of Finite Classical Groups
Author: Mikko KorhonenPublisher: Springer Nature
ISBN: 3031629159
Category :
Languages : en
Pages : 303
Book Description
The Maximal Subgroups of the Low-Dimensional Finite Classical Groups
Author: John N. BrayPublisher: Cambridge University Press
ISBN: 0521138604
Category : Mathematics
Languages : en
Pages : 453
Book Description
Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.
The Subgroup Structure of the Finite Classical Groups
Author: Peter B. KleidmanPublisher: Cambridge University Press
ISBN: 052135949X
Category : Mathematics
Languages : en
Pages : 317
Book Description
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.
Applying the Classification of Finite Simple Groups
Author: Stephen D. SmithPublisher: American Mathematical Soc.
ISBN: 1470442914
Category : Mathematics
Languages : en
Pages : 248
Book Description
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
The Maximal Subgroups of Classical Algebraic Groups
Author: Gary M. SeitzPublisher: American Mathematical Soc.
ISBN: 0821824279
Category : Linear algebraic groups
Languages : en
Pages : 294
Book Description
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.
Irreducible Subgroups of Exceptional Algebraic Groups
Author: Donna M. TestermanPublisher: American Mathematical Soc.
ISBN: 0821824538
Category : Embeddings
Languages : en
Pages : 198
Book Description
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.
Irreducible Geometric Subgroups of Classical Algebraic Groups
Author: Timothy C. Burness,Publisher: American Mathematical Soc.
ISBN: 1470414945
Category : Mathematics
Languages : en
Pages : 100
Book Description
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 .
Classes of Finite Groups
Author: Adolfo Ballester-BolinchesPublisher: Springer Science & Business Media
ISBN: 1402047193
Category : Mathematics
Languages : en
Pages : 391
Book Description
This book covers the latest achievements of the Theory of Classes of Finite Groups. It introduces some unpublished and fundamental advances in this Theory and provides a new insight into some classic facts in this area. By gathering the research of many authors scattered in hundreds of papers the book contributes to the understanding of the structure of finite groups by adapting and extending the successful techniques of the Theory of Finite Soluble Groups.
Proceedings of the Conference on Finite Groups
Author: William R. ScottPublisher: Academic Press
ISBN: 1483261085
Category : Mathematics
Languages : en
Pages : 580
Book Description
Proceedings of the Conference on Finite Groups provides information pertinent to the fundamental aspects of finite group theory. This book presents the problem of characterizing simple groups in terms of the local structure of a group. Organized into five parts encompassing 43 chapters, this book begins with an overview of the characterization of the Chevalley groups over fields of odd order and indicates the role of this characterization in the theory of component type groups. This text then examines the structure as well as the representations of specific simple groups. Other chapters consider the general theory of representations and characters of finite groups. This book discusses as well permutation groups and the connection between group theory and geometry. The final chapter deals with finite solvable groups as well as the theory of formations. This book is a valuable resource for mathematicians, graduate students, and research workers.