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Groups and Symmetry : Undergraduate Texts in Mathematics - Mark A. Armstrong

Groups and Symmetry

Undergraduate Texts in Mathematics

Hardcover

Published: 27th February 1997
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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.

M.A. Armstrong

Groups and Symmetry

"This book is a gentle introductory text on group theory and its application to the measurement of symmetry. It covers most of the material that one might expect to see in an undergraduate course . . . The theory is amplified, exemplified and properly related to what this part of algebra is really for by discussion of a wide variety of geometrical phenomena in which groups measure symmetry. Overall, the author's plan, to base his treatment on the premise that groups and symmetry go together, is a very good one, and the book deserves to succeed."-MATHEMATICAL REVIEWS

Preface
Symmetries of the Tetrahedron
Axioms
Numbers
Dihedral Groups
Subgroups and Generators
Permutations
Isomorphisms
Plato's Solids and Cayley's Theorem
Matrix Groups
Products
Lagrange's Theorem
Partitions
Cauchy's Theorem
Conjugacy
Quotient Groups
Homomorphisms
Actions, Orbits, and Stabalizers
Counting Orbits
Finite Rotation Groups
The Sylow Theorems
Finitely Generated Abelian Groups
Row and Column Operations
Automorphisms
The Euclidean Group
Lattices and Point Groups
Wallpaper Patterns
Free Groups and Presentations
Trees and the Nielsen-Schreier
Theorem
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387966755
ISBN-10: 0387966757
Series: Undergraduate Texts in Mathematics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 187
Published: 27th February 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 16.5  x 1.7
Weight (kg): 0.46
Edition Number: 2