Groups and Symmetry / Edition 1

Groups and Symmetry / Edition 1

4.0 1
by Mark A. Armstrong, M. A. Armstrong, Gerard Iooss
     
 

ISBN-10: 0387966757

ISBN-13: 9780387966755

Pub. Date: 10/25/1988

Publisher: Springer New York

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

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.

Product Details

ISBN-13:
9780387966755
Publisher:
Springer New York
Publication date:
10/25/1988
Series:
Undergraduate Texts in Mathematics Series
Edition description:
1st ed. 1988. Corr. 2nd printing 1997
Pages:
187
Product dimensions:
9.21(w) x 6.14(h) x 0.50(d)

Table of Contents

Preface. 1: Symmetries of the Tetrahedron. 2: Axioms. 3: Numbers. 4: Dihedral Groups. 5: Subgroups and Generators. 6: Permutations. 7: Isomorphisms. 8: Plato's Solids and Cayley's Theorem. 9: Matrix Groups. 10: Products. 11: Lagrange's Theorem. 12: Partitions. 13: Cauchy's Theorem. 14: Conjugacy. 15: Quotient Groups. 16: Homomorphisms. 17: Actions, Orbits, and Stabalizers. 18: Counting Orbits. 19: Finite Rotation Groups. 20: The Sylow Theorems. 21: Finitely Generated Abelian Groups. 22: Row and Column Operations. 23: Automorphisms. 24: The Euclidean Group. 25: Lattices and Point Groups. 26: Wallpaper Patterns. 27: Free Groups and Presentations. 28: Trees and the Nielsen-Schreier Theorem. Bibliography. Index.

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Groups and Symmetry 4 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
dealing with an abstract area on a geometrical basis is very interesting - makes it tangible - the exercises are literally 'hands-on' - don't xpect rigorous stuff