Groups and Characters / Edition 1

Hardcover (Print)
Buy New
Buy New from BN.com
$142.76
Used and New from Other Sellers
Used and New from Other Sellers
from $148.49
Usually ships in 1-2 business days
(Save 16%)
Other sellers (Hardcover)
  • All (9) from $148.49   
  • New (4) from $148.49   
  • Used (5) from $179.98   

Overview

A lively and thorough textbook for graduate courses and general reference that illuminates the interdependence between group theory and representative/character theory. It includes an entire chapter of challenging and fully detailed examples, and there are exercises throughout the text that help readers prove for themselves its well-articulated points.
Read More Show Less

Editorial Reviews

Booknews
A textbook for a graduate mathematics course of one or two semesters. Combines group and character theory, with a focus on finite groups, and includes some computational aspects. Readers are assumed to have completed a graduate-level course in abstract algebra and have a reasonable facility with linear algebra. Also suitable as a reference for chemists, physicists, and crystallographers. Annotation c. by Book News, Inc., Portland, Or.
Read More Show Less

Product Details

Meet the Author

LARRY C. GROVE is Professor of Mathematics at the University of Arizona He is the author of Algebra and coauthor of Finite Reflection Groups.
Read More Show Less

Table of Contents

Preface
1 Preliminaries
1.1 Some Notation and Generalities 1
1.2 Permutation Actions 3
1.3 Coset Enumeration 9
1.4 Semidirect Products 13
1.5 Wreath Products 14
1.6 Transitivity and Primitivity 16
1.7 Some Linear Algebra 20
2 Some Groups
2.1 Aut(Z[subscript n]) 27
2.2 Metacyclic Groups 29
2.3 Sylow Subgroups of Symmetric Groups 30
2.4 Affine Groups of Fields 32
2.5 Finite Groups in 2 and 3 Dimensions 33
2.6 Some Linear Groups 39
2.7 Mathieu Groups 46
2.8 Symplectic Groups 52
3 Counting with Groups
3.1 Fixed Points and Orbits 61
3.2 The Cycle Index 64
3.3 Enumeration 68
3.4 Generating Functions 73
3.5 The Petersen Graph 75
4 Transfer and Splitting
4.1 Transfer and Normal Complements 77
4.2 Hall Subgroups 84
4.3 Mostly p-groups 89
5 Representations and Characters
5.1 Representations 97
5.2 Characters 105
5.3 Contragredients and Products 121
6 Induction and Restriction
6.1 Modules 127
6.2 Induction 128
6.3 Normal Subgroups and Clifford Theory 136
6.4 Mackey Theorems 142
6.5 Brauer Theorems 147
7 Computing Character Tables
7.1 Burnside 151
7.2 Dixon 154
7.3 Schneider 158
8 Characters of S[subscript n] and A[subscript n]
8.1 Symmetric Groups 161
8.2 Alternating Groups 168
9 Frobenius Groups
9.1 Frobenius Groups and Their Characters 171
9.2 Structure of Frobenius Groups 176
10 Splitting Fields
10.1 Splitting 183
10.2 The Schur Index 184
10.3 R versus C 190
Bibliography 203
Index 209
Read More Show Less

Customer Reviews

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

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com 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 & Noble.com 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 & Noble.com 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 BN.com 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

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com 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 BN.com. 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)