Groups and Symmetry

Groups and Symmetry

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This is 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. Includes more than 300 exercises and approximately 60 illustrations.

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Product details

  • Hardback | 187 pages
  • 160.02 x 238.76 x 17.78mm | 453.59g
  • Springer-Verlag New York Inc.
  • New York, NY, United States
  • English
  • 1st ed. 1988. Corr. 2nd printing 1997
  • 1, black & white illustrations
  • 0387966757
  • 9780387966755
  • 390,114

Review quote

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

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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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