# Groups and Symmetry

Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the vocabulary and many of 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

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## Overview

Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the vocabulary and many of 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, emphasis is placed on concrete examples, often geometrical in nature, so that finite rotation groups and the 17 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 groups actions on trees. There are more than 300 exercises and approximately 60 illustrations to help develop the student's intuition.

## Editorial Reviews

From the Publisher
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

Booknews
Textbook introduces the vocabulary and some highlights of elementary group theory. Emphasis is placed on concrete examples so that finite rotation groups and the 17 wallpaper groups are treated in detail alongside theoretical results. Over 300 exercises and some 60 illustrations. Annotation c. Book News, Inc., Portland, OR (booknews.com)

## Product Details

ISBN-13:
9781441930859
Publisher:
Springer New York
Publication date:
12/01/2010
Series:
Undergraduate Texts in Mathematics Series, #1
Edition description:
Softcover reprint of hardcover 1st ed. 1988
Pages:
187
Product dimensions:
0.43(w) x 9.21(h) x 6.14(d)

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