Representations of Groups: A Computational Approach

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $70.21
Usually ships in 1-2 business days
(Save 21%)
Other sellers (Hardcover)
  • All (8) from $70.21   
  • New (6) from $70.21   
  • Used (2) from $89.98   


The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from and readers can download source code and solutions to selected exercises from the book's web page.

Read More Show Less

Editorial Reviews

From the Publisher
"Representations of Groups: A Computational Approach, by Lux and Pahlings, is a well-constructed, dense, and, its introductory nature notwithstanding, pretty far-reaching text. Happily, it is also quite accessible....As it should be given what the authors have in mind, Representations of Groups: A Computational Approach is laden with examples and exercises, many of them supplied with hints. The book is well-written and anything but chatty and is based on the authors’ courses so that much of the material in the book has been field tested."
Michael Berg, MAA Reviews

"I enjoyed reading this book, and recommend it as a good modern second course in representation theory. The choice of topics and their arrangement are interesting, sometimes even surprising, but clearly well thought out."
Robert A. Wilson, Bulletin of the London Mathematical Society

"... this is really a wonderful, nice, and significant book, which is so well written, and it is recommended to a wide range of mathematicians, including not only graduate students but also many mathematicians of greater experience."
Shigeo Koshittani, Mathematical Reviews

Read More Show Less

Product Details

Meet the Author

Klaus Lux is Associate Professor in the Department of Mathematics at the University of Arizona, Tucson.

Herbert Pahlings is Professor Emeritus at RWTH Aachen University in Germany.

Read More Show Less

Table of Contents

Preface vii

List of frequently used symbols x

1 Representations and modules 1

1.1 Basic concepts 1

1.2 Permutation representations and G-sets 23

1.3 Simple modules, the "Meataxe" 36

1.4 Structure of algebras 50

1.5 Semisimple rings and modules 55

1.6 Direct sums and idempotents 63

1.7 Blocks 79

1.8 Changing coefficients 83

2 Characters 87

2.1 Characters and block idempotents 87

2.2 Character values 101

2.3 Character degrees 109

2.4 The Dixon-Schneider algorithm 113

2.5 Application - generation of groups 121

2.6 Character tables 135

2.7 Products of characters 139

2.8 Generalized characters and lattices 149

2.9 Invariant bilinear forms and the Schur index 164

2.10 Computing character tables - an example 173

3 Groups and subgroups 179

3.1 Restriction and fusion 179

3.2 Induced modules and characters 182

3.3 Symmetric groups 199

3.4 Permutation characters 206

3.5 Tables of marks 210

3.6 Clifford theory 223

3.7 Projective representations 238

3.8 Clifford matrices 259

3.9 M-groups 277

3.10 Brauer's induction theorem 281

4 Modular representations 289

4.1 p-modular systems 289

4.2 Brauer characters 301

4.3 p-projective characters 315

4.4 Characters in blocks 321

4.5 Basic sets 331

4.6 Defect groups 344

4.7 Brauer correspondence 350

4.8 Vertices 365

4.9 Green correspondence 378

4.10 Trivial source modules 386

4.11 Generalized decomposition numbers 396

4.12 Brauer's theory of blocks of defect one 407

4.13 Brauer characters of p-solvable groups 422

4.14 Some conjectures 426

References 443

Notation index 455

Subject index 457

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)