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Product Details
From the back cover: "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 the Nielsen-Schreier theorem, using group actions on trees. There are more than 300 exercises and approximately 60 illustrations to help develop the student's intuition."
BRIEF CONTENTS
Preface
Chapter 1 - Symmetries of the Tetrahedron
Chapter 2 - Axioms
Chapter 3 - Numbers
Chapter 4 - Dihedral Groups
Chapter 5 - Subgroups and Generators
Chapter 6 - Permutations
Chapter 7 - Isomorphisms
Chapter 8 - Plato's Solids and Cayley's Theorem
Chapter 9 - Matrix Groups
Chapter 10 - Products
Chapter 11 - Lagrange's Theorem
Chapter 12 - Partitions
Chapter 13 - Cauchy's Theorem
Chapter 14 - Conjugacy
Chapter 15 - Quotient Groups
Chapter 16 - Homomorphisms
Chapter 17 - Actions, Orbits, and Stabilizers
Chapter 18 - Counting Orbits
Chapter 19 - Finite Rotation Groups
Chapter 20 - The Sylow Theorems
Chapter 21 - Finitely Generated Abelian Groups
Chapter 22 - Row and Column Operations
Chapter 23 - Automorphisms
Chapter 24 - The Euclidean Group
Chapter 25 - Lattices and Point Groups
Chapter 26 - Wallpaper Patterns
Chapter 27 - Free Groups and Presentations
Chapter 28 - Trees and the Nielsen-Schreier Theorem
