2 edition of **On the modular representations of groups of finite order** found in the catalog.

On the modular representations of groups of finite order

Richard Brauer

- 362 Want to read
- 6 Currently reading

Published
**1937**
by University of Toronto Press in Toronto
.

Written in English

- Group theory.

**Edition Notes**

Bibliographical footnotes.

Other titles | Modular representations of groups of finite order. |

Statement | by B. Brauer and C. Nesbitt. |

Series | Toronto. University. Studies. Mathematical series -- no. 4., University of Toronto studies -- no. 4. |

Contributions | Nesbitt, Cecil James, 1912- |

The Physical Object | |
---|---|

Pagination | pts. |

ID Numbers | |

Open Library | OL16603575M |

The earliest work on representation theory over finite fields is by Dickson () who showed that when p does not divide the order of the group, the representation theory is similar to that in characteristic 0. He also investigated modular invariants of some finite groups. At the crossroads of representation theory, algebraic geometry and finite group theory, this book blends together many of the main concerns of modern algebra, with full proofs of some of the most remarkable achievements in the by:

Free 2-day shipping. Buy Modular Representation Theory of Finite Groups (Paperback) at The book under review is an introduction to the modular representation theory of finite groups with a somehow balanced approach to the subject. It develops enough ring and module theoretic methods to treat Green’s theory of indecomposable representations, the Grothendieck group of the group algebra k[G], its ring structure, the Burnside ring.

The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. Modular Representations of Finite Groups of Lie Type () by J E Humphreys Add To MetaCart. Tools. Sorted by We prove that an element g of prime order> 3 belongs to the solvable radical R(G) of a finite (or, more generally, a linear) group if and only if for every x ∈ G the subgroup generated by g, xgx −1 is solvable.

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The book under review is an introduction to the modular representation theory of finite groups with a somehow balanced approach to the subject. the book is almost self-contained. It has the lightness of a gentle-paced lecture course and could be used with profit for an introduction to the methods of representation theory of finite groups, either in a formal course or for self Cited by: Finite groups of Lie type encompass most of the finite simple groups.

Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved.

This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime by: This volume contains a concise exposition of the theory of finite groups, including the theory of modular representations.

The rudiments of linear algebra and knowledge of the elementary concepts of group theory are useful, if not entirely indispensable, prerequisites for reading this book; most of the other requisites, such as the theory of p -adic fields, are developed in the by: Modular Representation Theory of finite Groups comprises this second situation.

Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. Modular representation theory of finite groups comprises this second situation.

Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading On the modular representations of groups of finite order book the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations.

Modular Representations of Finite Groups (Pure and Applied Mathematics (Academic Press), Volume 73) | B. Puttaswamaiah, John D.

Dixon | download | B–OK. Download books for free. Find books. Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.

It contains research works in the areas of modular representation theory of p-adic groups and finite groups and their related algebras. The aim of this volume is to provide a bridge — where interactions are rare between researchers from these two areas — by highlighting the latest developments, suggesting potential new research problems, and promoting new.

Modular Representation Theory (Classical) Characters As before, G is a ﬁnite reductive group, e the order of q mod ` SURPRISE: Brauer Theory and Lusztig Theory are compatible. e(q) is the e-th cyclotomic polynomial. The order of G is the -modular Representations of Finite Reductive GroupsFile Size: KB.

For groups of prime power order the situation C.B. Thomas / Modular representations is more promising, but since in order to obtain a non-trivial representation ring we must then take (q, I GI) = 1, when FqG is semisimple, the solution is likely to be similar to that for C, see [10].Author: Charles B.

Thomas. On the modular representations of groups of finite order. Toronto, University of Toronto Press, (OCoLC) Document Type: Book: All Authors / Contributors: Richard Brauer. Abstract. We are now ready to apply the results from the previous chapter to group rings of finite groups.

If the order of the group is invertible in the base field, Maschke’s Theorem tells us that the group ring is semisimple, and semisimple rings are of less interest from the homological algebra point of : Alexander Zimmermann. Purchase Modular Representations of Finite Groups, Volume 73 - 1st Edition.

Print Book & E-Book. ISBNBook Edition: 1. Modular Representations of Finite Groups of Lie Type (London Mathematical Society Lecture Note Series Book ) - Kindle edition by Humphreys, James E.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Modular Representations of Finite Groups of Lie Type (London Price: $ After a short review of background material, three closely connected topics in modular representation theory of finite groups are treated: representations rings, almost split sequences and the Auslander-Reiten quiver, complexity and cohomology varieties.

The last of these has become a major theme in representation theory into Cited by: Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups.

Organized into five chapters, this book begins with an overview of the basic facts about rings and Edition: 1. JOURNAL OF ALGE () Modular Representations of p Groups SHEILA BRENNER Department of Applied Mathematics, University of Liverpool Communicated by J.

Green Received June 4, l. INTRODUCTION Let G be an Abelian p group, k a field of characteristic^), and E a k by: Book description. The aim of this text is to present some of the key results in the representation theory of finite groups.

In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory by: COVID Resources.

Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

thereby giving representations of the group on the homology groups of the space. If there is torsion in the homology these representations require something other than ordinary character theory to be understood.

This book is written for students who are studying nite group representation theory beyond the level of a rst course in abstract Size: 1MB.

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 Edition: 1.Modular Representation Theory (Classical) Characters Richard Brauer developed the modular representation theory of ﬁnite groups, starting in the thirties.

G a ﬁnite group p a prime integer K a suﬃciently large ﬁeld of characteristic 0 O a complete discrete valuation ring with quotient ﬁeld K k residue ﬁeld of O, char k=p.Get this from a library! Modular representations of finite groups. [B M Puttaswamaiah; John D Dixon] -- The purpose of this book is to give a direct and readable account of the basic concepts and techniques of the theory of modular representations of finite groups .