# Groups and Symmetry

• M. A. Armstrong
Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xi
2. M. A. Armstrong
Pages 1-5
3. M. A. Armstrong
Pages 6-10
4. M. A. Armstrong
Pages 11-14
5. M. A. Armstrong
Pages 15-19
6. M. A. Armstrong
Pages 20-25
7. M. A. Armstrong
Pages 26-31
8. M. A. Armstrong
Pages 32-36
9. M. A. Armstrong
Pages 37-43
10. M. A. Armstrong
Pages 44-51
11. M. A. Armstrong
Pages 52-56
12. M. A. Armstrong
Pages 57-60
13. M. A. Armstrong
Pages 61-67
14. M. A. Armstrong
Pages 68-72
15. M. A. Armstrong
Pages 73-78
16. M. A. Armstrong
Pages 79-85
17. M. A. Armstrong
Pages 86-90
18. M. A. Armstrong
Pages 91-97
19. M. A. Armstrong
Pages 98-103
20. M. A. Armstrong
Pages 104-112
21. M. A. Armstrong
Pages 113-118
22. M. A. Armstrong
Pages 119-124
23. M. A. Armstrong
Pages 125-130
24. M. A. Armstrong
Pages 131-135
25. M. A. Armstrong
Pages 136-144
26. M. A. Armstrong
Pages 145-154
27. M. A. Armstrong
Pages 155-165
28. M. A. Armstrong
Pages 166-172
29. M. A. Armstrong
Pages 173-180
30. Back Matter
Pages 181-187

### Introduction

Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea. Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the seventeen wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using group actions on trees. There are more than three hundred exercises and approximately sixty illustrations to help develop the student's intuition.

### Keywords

Abelian group Group theory Lattice Point group automorphism group action

#### Authors and affiliations

• M. A. Armstrong
• 1
1. 1.Department of Mathematical SciencesUniversity of DurhamDurhamEngland

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-4034-9
• Copyright Information Springer-Verlag New York 1988
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4419-3085-9
• Online ISBN 978-1-4757-4034-9
• Series Print ISSN 0172-6056
• Buy this book on publisher's site