# A First Course in Group Theory

Textbook

Part of the Universitext book series (UTX)

1. Front Matter
Pages i-ix
2. Cyril F. Gardiner
Pages 1-10
3. Cyril F. Gardiner
Pages 11-35
4. Cyril F. Gardiner
Pages 36-50
5. Cyril F. Gardiner
Pages 51-100
6. Cyril F. Gardiner
Pages 101-118
7. Cyril F. Gardiner
Pages 119-129
8. Cyril F. Gardiner
Pages 130-170
9. Cyril F. Gardiner
Pages 171-188
10. Back Matter
Pages 189-227

### Introduction

One of the difficulties in an introductory book is to communicate a sense of purpose. Only too easily to the beginner does the book become a sequence of definitions, concepts, and results which seem little more than curiousities leading nowhere in particular. In this book I have tried to overcome this problem by making my central aim the determination of all possible groups of orders 1 to 15, together with some study of their structure. By the time this aim is realised towards the end of the book, the reader should have acquired the basic ideas and methods of group theory. To make the book more useful to users of mathematics, in particular students of physics and chemistry, I have included some applications of permutation groups and a discussion of finite point groups. The latter are the simplest examples of groups of partic­ ular interest to scientists. They occur as symmetry groups of physical configurations such as molecules. Many ideas are discussed mainly in the exercises and the solutions at the end of the book. However, such ideas are used rarely in the body of the book. When they are, suitable references are given. Other exercises test and reinfol:'ce the text in the usual way. A final chapter gives some idea of the directions in which the interested reader may go after working through this book. References to help in this are listed after the outline solutions.

### Keywords

Abelian group Group theory Gruppe (Math.) Point group Symmetry group

#### Authors and affiliations

1. 1.Department of MathematicsUniversity of ExeterExeterEngland

### Bibliographic information

• Book Title A First Course in Group Theory
• Authors Cyril F. Gardiner
• Series Title Universitext
• DOI https://doi.org/10.1007/978-1-4613-8117-4
• Copyright Information Springer-Verlag New York 1980
• Publisher Name Springer, New York, NY
• eBook Packages
• Softcover ISBN 978-0-387-90545-7
• eBook ISBN 978-1-4613-8117-4
• Series ISSN 0172-5939
• Series E-ISSN 2191-6675
• Edition Number 1
• Number of Pages X, 228
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site