Theory of Groups of Finite Order
Title | Theory of Groups of Finite Order PDF eBook |
Author | William Burnside |
Publisher | |
Pages | 420 |
Release | 1897 |
Genre | Group theory |
ISBN |
K-Theory of Finite Groups and Orders
Title | K-Theory of Finite Groups and Orders PDF eBook |
Author | Richard G. Swan |
Publisher | Springer |
Pages | 238 |
Release | 1986-01-01 |
Genre | Mathematics |
ISBN | 9783540049388 |
These notes are from a course given at the University of Chicago. No pretense of completeness is made. A great deal of additional material may be found in Bass' book [BK] which gives a remarkably complete account of algebraic K-theory. The present notes, however, contain a number of recent results of Jacobinski [J] and Roiter [R]. An excellent survey of the theory of orders with detailed references may be found in Reiner's article [RS].
Finite Group Theory
Title | Finite Group Theory PDF eBook |
Author | I. Martin Isaacs |
Publisher | American Mathematical Society |
Pages | 368 |
Release | 2023-01-24 |
Genre | Mathematics |
ISBN | 1470471604 |
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.
Finite Group Theory
Title | Finite Group Theory PDF eBook |
Author | M. Aschbacher |
Publisher | Cambridge University Press |
Pages | 320 |
Release | 2000-06-26 |
Genre | Mathematics |
ISBN | 9780521786751 |
The book provides the basic foundations for the local theory of finite groups, the theory of classical linear groups, and the theory of buildings and BN-pairs.
Theory of Groups of Finite Order - Scholar's Choice Edition
Title | Theory of Groups of Finite Order - Scholar's Choice Edition PDF eBook |
Author | William Burnside |
Publisher | Scholar's Choice |
Pages | 418 |
Release | 2015-02-11 |
Genre | |
ISBN | 9781294968863 |
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Theory of Finite Groups
Title | The Theory of Finite Groups PDF eBook |
Author | Hans Kurzweil |
Publisher | Springer Science & Business Media |
Pages | 389 |
Release | 2003-11-06 |
Genre | Mathematics |
ISBN | 0387405100 |
From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews
A Course in Finite Group Representation Theory
Title | A Course in Finite Group Representation Theory PDF eBook |
Author | Peter Webb |
Publisher | Cambridge University Press |
Pages | 339 |
Release | 2016-08-19 |
Genre | Mathematics |
ISBN | 1107162394 |
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.