Last edited by Dihn
Thursday, July 30, 2020 | History

5 edition of Theory of Blocks of the Finite Groups found in the catalog.

Theory of Blocks of the Finite Groups

by Lluis Puig

  • 161 Want to read
  • 24 Currently reading

Published by Springer .
Written in English,

    Subjects:
  • Groups & group theory,
  • Mathematics,
  • Science/Mathematics,
  • Group Theory,
  • Mathematics / Group Theory,
  • Blocks (Group theory),
  • Finite Groups

  • The Physical Object
    FormatHardcover
    Number of Pages209
    ID Numbers
    Open LibraryOL9057716M
    ISBN 10354043514X
    ISBN 109783540435143

    This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume. 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.

    Characters and blocks of finite groups. [G Navarro] -- Research text on algebra/representation theory. a strong pedagogical work and a worthy sequel to Isaacs' book on ordinary character theory." Bulletin of the AMS " a Read more User-contributed reviews. Tags. Add tags for "Characters and blocks. solvable groups all of whose 2-local subgroups are solvable. The reader will realize that nearly all of the methods and results of this book are used in this investigation. At least two things have been excluded from this book: the representation theory of finite groups and—with a few exceptions—the description of the finite simple groups.

      Project Gutenberg’s Theory of Groups of Finite Order, by William Burnside This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. It is aimed at graduate students, with previous knowledge of ordinary character theory, and researchers interested in the representation theory of finite groups.


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Theory of Blocks of the Finite Groups by Lluis Puig Download PDF EPUB FB2

About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzero characteristic p: any indecomposable two-sided ideal that also is a direct summand of kG determines a G-block.

In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail.

In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein Cited by: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory.

The two volumes take into account classical results and concepts as well as some of the modern developments in the by: 3. The block theory of finite group algebras. Vol.2 | Linckelmann, Markus | download | B–OK. Download books for free.

Find books. This book is a unique survey of the whole field of modular representation theory of finite groups. The main topics are block theory and module theory of group representations, including blocks with cyclic defect groups, symmetric groups, groups of Lie type, local-global : Springer International Publishing.

This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures.

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.

Ordinary induction from a subgroup and finite group block theory Harris, Morton E., Osaka Journal of Mathematics, ; On the Dade character correspondence and isotypies between blocks of finite groups Watanabe, Atumi, Osaka Journal of Mathematics,   Markus Linckelmann, The block theory of finite group algebras (2 vols), London Mathematical Society Student Texts, vol.

91–92, Cambridge University Press, Cambridge, CrossRef Google Scholar The Theory of Groups of Finite Order, originally published inwas the first major textbook on the subject. The second edition (reissued here) contains an account of Frobenius's character theory, and remained the standard reference for many by: Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods.

Theory of Finite Simple Groups This book provides the first representation theoretic and algorithmic approach to the theory of abstract finite simple groups. Together with the cyclic groups of prime order the finite simple groups are the building blocks of all finite groups.

The. This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint.

After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks. The finite simple groups can be seen as the basic building blocks of all finite groups, in a way reminiscent of the way the prime numbers are the basic building blocks of the natural numbers.

The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups. Buy The Block Theory of Finite Group Algebras 2 Paperback Book Set (London Mathematical Society Student Texts) on FREE SHIPPING on qualified orders. "The book under review is incontrovertible proof that the theory of finite groups per se is alive and well too.

is also a marvelous treatment of a large chunk of what is going on today. There are a lot of nice exercises, the scholarship is phenomenally thorough. The entire presentation is quite elegant.

Cited by: Character theory of finite groups I. Martin Isaacs In addition to techniques for applying characters to "pure" group theory, much of the book focuses on properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. Problems follow each chapter.

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic.

Group theory is central to many areas of pure and applied mathematics and the classification. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions.

One who completes this text not only gains an appreciation of both the depth and the breadth of the theory of finite groups, but also witnesses the evolutionary development of concepts.

Graduate students and researchers in modular representation theory, especially block theory, will find this systematic introduction indispensable.

The two volumes include detailed treatments of classic material as well as more modern developments which have not appeared in any book before, giving readers a comprehensive overview of the subject. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange.Block Theory of Finite Group Algebras: Volume 2 Markus Linckelmann This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory.

The two volumes take into account classical results and concepts as well as some of the modern developments in the area.Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these properties reflect and are reflected in the structure of the group.