A Course on Finite Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course on Finite Groups write by H.E. Rose. This book was released on 2009-12-16. A Course on Finite Groups available in PDF, EPUB and Kindle. Introduces the richness of group theory to advanced undergraduate and graduate students, concentrating on the finite aspects. Provides a wealth of exercises and problems to support self-study. Additional online resources on more challenging and more specialised topics can be used as extension material for courses, or for further independent study.
A Course in Finite Group Representation Theory
A Course in Finite Group Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in Finite Group Representation Theory write by Peter Webb. This book was released on 2016-08-19. A Course in Finite Group Representation Theory available in PDF, EPUB and Kindle. 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.
The Form of Finite Groups
The Form of Finite Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Form of Finite Groups write by Stephen G Odaibo M D. This book was released on 2016-01-02. The Form of Finite Groups available in PDF, EPUB and Kindle. Group theory is the language in which our natural world is expressed. Everything from Einstein's theory of relativity to the inner workings of electrons, protons, and quarks are encoded in the language of group theory. This book on finite group theory is a great resource for both undergraduate and graduate students in the Mathematical sciences. It will also be found indispensable by anyone serious about acquiring a fundamental understanding of our physical world.
Finite Group Theory
Finite Group Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Group Theory write by I. Martin Isaacs. This book was released on 2023-01-24. Finite Group Theory available in PDF, EPUB and Kindle. 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.
Character Theory of Finite Groups
Character Theory of Finite Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Character Theory of Finite Groups write by I. Martin Isaacs. This book was released on 2006-11-21. Character Theory of Finite Groups available in PDF, EPUB and Kindle. Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group. The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging. In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters. This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.
