**Classroom Resource Materials**

Volume: 32;
2009;
295 pp;
Softcover

**Print ISBN: 978-1-4704-6433-2
Product Code: CLRM/32.S**

List Price: $75.00

AMS Member Price: $56.25

MAA Member Price: $56.25

**Electronic ISBN: 978-1-61444-102-1
Product Code: CLRM/32.E**

List Price: $75.00

AMS Member Price: $56.25

MAA Member Price: $56.25

# Visual Group Theory

Share this page
*Nathan Carter*

MAA Press: An Imprint of the American Mathematical Society

Recipient of the Mathematical Association of America's
Beckenbach Book Prize in 2012!

Group theory is the branch of mathematics that
studies symmetry, found in crystals, art, architecture, music and many
other contexts, but its beauty is lost on students when it is taught
in a technical style that is difficult to understand. Visual Group
Theory assumes only a high school mathematics background and
covers a typical undergraduate course in group theory from a
thoroughly visual perspective. The more than 300 illustrations in
Visual Group Theory bring groups, subgroups, homomorphisms,
products, and quotients into clear view. Every topic and theorem is
accompanied with a visual demonstration of its meaning and import,
from the basics of groups and subgroups through advanced structural
concepts such as semidirect products and Sylow theory.

#### Reviews & Endorsements

Carter presents the group theory portion of abstract algebra in a way that allows students to actually see, using a multitude of examples and applications, the basic concepts of group theory … The numerous images (more than 300) are the heart of the text. As this work enables readers to see, experiment with, and understand the significance of groups, they will accumulate examples of groups and their properties that will serve them well in future endeavors in mathematics. Recommended.

-- J. T. Zerger, Choice

If you teach abstract algebra, then this book should be a part of the resources you use. While the phrase “visual abstract algebra” may seem to be a contradiction, the diagrams in this book are an existence proof to the contrary. They are clear, colorful and concise, very easy to understand and sure to aid the students that have difficulty in internalizing the abstract nature of the subject matter …

-- Charles Ashbacher, Journal of Recreational Mathematics

# Table of Contents

## Visual Group Theory

- cover cover11
- title page iii4
- copyright page ii3
- Acknowledgments vii8
- Preface ix10
- Contents xi12
- Overview 116
- What is a group? 318
- What do groups look like? 1126
- Why study groups? 2540
- Algebra at last 4156
- Five families 6378
- Subgroups 97112
- Products and quotients 117132
- The power of homomorphisms 157172
- Sylow theory 193208
- Galois theory 221236
- Answers to selected Exercises 261276
- Bibliography 285300
- Index of Symbols Used 287302
- Index 288303
- About the Author 297312
- Back cover 298313