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On Finite Permutation Groups
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Book Synopsis Permutation Groups by : John D. Dixon
Download or read book Permutation Groups written by John D. Dixon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the basic ideas, standard constructions and important examples in the theory of permutation groups, the book goes on to develop the combinatorial and group theoretic structure of primitive groups leading to the proof of the pivotal ONan-Scott Theorem which links finite primitive groups with finite simple groups. Special topics covered include the Mathieu groups, multiply transitive groups, and recent work on the subgroups of the infinite symmetric groups. With its many exercises and detailed references to the current literature, this text can serve as an introduction to permutation groups in a course at the graduate or advanced undergraduate level, as well as for self-study.
Book Synopsis Finite Permutation Groups by : Helmut Wielandt
Download or read book Finite Permutation Groups written by Helmut Wielandt and published by Academic Press. This book was released on 2014-05-10 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.
Book Synopsis Permutation Group Algorithms by : Ákos Seress
Download or read book Permutation Group Algorithms written by Ákos Seress and published by Cambridge University Press. This book was released on 2003-03-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Book Synopsis Permutation Groups and Combinatorial Structures by : Norman Biggs
Download or read book Permutation Groups and Combinatorial Structures written by Norman Biggs and published by Cambridge University Press. This book was released on 1979-08-16 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the action of permutation groups on sets associated with combinatorial structures. Each chapter deals with a particular structure: groups, geometries, designs, graphs and maps respectively. A unifying theme for the first four chapters is the construction of finite simple groups. In the fifth chapter, a theory of maps on orientable surfaces is developed within a combinatorial framework. This simplifies and extends the existing literature in the field. The book is designed both as a course text and as a reference book for advanced undergraduate and graduate students. A feature is the set of carefully constructed projects, intended to give the reader a deeper understanding of the subject.
Book Synopsis Permutation Groups by : Peter J. Cameron
Download or read book Permutation Groups written by Peter J. Cameron and published by Cambridge University Press. This book was released on 1999-02-04 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes recent developments in the study of permutation groups for beginning graduate students.
Book Synopsis Applied Discrete Structures by : Ken Levasseur
Download or read book Applied Discrete Structures written by Ken Levasseur and published by Lulu.com. This book was released on 2012-02-25 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: ''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''--
Book Synopsis Permutation Groups and Cartesian Decompositions by : Cheryl E. Praeger
Download or read book Permutation Groups and Cartesian Decompositions written by Cheryl E. Praeger and published by London Mathematical Society Le. This book was released on 2018-05-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise introduction to permutation groups, focusing on invariant cartesian decompositions and applications in algebra and combinatorics.
Book Synopsis Finite Group Theory by : I. Martin Isaacs
Download or read book Finite Group Theory written by I. Martin Isaacs and published by American Mathematical Society. This book was released on 2023-01-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur–Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the “principal ideal theorem” of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Pólya Lecturer in 2003–2005.
Book Synopsis Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups by : Nick Gill
Download or read book Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups written by Nick Gill and published by Springer Nature. This book was released on 2022-06-17 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a proof of Cherlin’s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan’s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin’s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest to a wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.
Book Synopsis Permutation Groups by : Donald S. Passman
Download or read book Permutation Groups written by Donald S. Passman and published by Courier Corporation. This book was released on 2013-10-03 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes by a prominent authority provide a self-contained account of classification theorems. Includes work of Zassenhaus on Frobenius elements and sharply transitive groups, Huppert's theorem, more. 1968 edition.
Book Synopsis Groups, Combinatorics and Geometry by : Martin W. Liebeck
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.
Book Synopsis Theory of Groups of Finite Order by : William S. Burnside
Download or read book Theory of Groups of Finite Order written by William S. Burnside and published by Courier Corporation. This book was released on 2013-02-20 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic 1911 edition covers many group-related properties, including an extensive treatment of permutation groups and groups of linear substitutions, along with graphic representation of groups, congruence groups, and special topics.
Book Synopsis Representation Theory of Finite Groups by : Martin Burrow
Download or read book Representation Theory of Finite Groups written by Martin Burrow and published by Academic Press. This book was released on 2014-05-10 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.
Book Synopsis Regular Subgroups of Primitive Permutation Groups by : Martin W. Liebeck
Download or read book Regular Subgroups of Primitive Permutation Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addresses the classical problem of determining finite primitive permutation groups G with a regular subgroup B.
Book Synopsis Finite Structures with Few Types by : Gregory L. Cherlin
Download or read book Finite Structures with Few Types written by Gregory L. Cherlin and published by Princeton University Press. This book was released on 2003 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups. Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory, classical geometries, and combinatorics. The principal results are finite theorems, an associated analysis of computational issues, and an "intrinsic" characterization of the permutation groups (or finite structures) under consideration. The main finiteness theorem shows that the structures under consideration fall naturally into finitely many families, with each family parametrized by finitely many numerical invariants (dimensions of associated coordinating geometries). The authors provide a case study in the extension of methods of stable model theory to a nonstable context, related to work on Shelah's "simple theories." They also generalize Lachlan's results on stable homogeneous structures for finite relational languages, solving problems of effectivity left open by that case. Their methods involve the analysis of groups interpretable in these structures, an analog of Zilber's envelopes, and the combinatorics of the underlying geometries. Taking geometric stability theory into new territory, this book is for mathematicians interested in model theory and group theory.
Book Synopsis Finite Group Theory by : M. Aschbacher
Download or read book Finite Group Theory written by M. Aschbacher and published by Cambridge University Press. This book was released on 2000-06-26 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 40 years the theory of finite groups has developed dramatically. The finite simple groups have been classified and are becoming better understood. Tools exist to reduce many questions about arbitrary finite groups to similar questions about simple groups. Since the classification there have been numerous applications of this theory in other branches of mathematics. Finite Group Theory develops the foundations of the theory of finite groups. It can serve as a text for a course on finite groups for students already exposed to a first course in algebra. It could supply the background necessary to begin reading journal articles in the field. For specialists it also provides a reference on the foundations of the subject. This second edition has been considerably improved with a completely rewritten Chapter 15 considering the 2-Signalizer Functor Theorem, and the addition of an appendix containing solutions to exercises.
Book Synopsis Visual Group Theory by : Nathan Carter
Download or read book Visual Group Theory written by Nathan Carter and published by American Mathematical Soc.. This book was released on 2021-06-08 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
