Armstrong M.A. Groups and Symmetry

Springer, 1988. — 197 p. — (Undergraduate Texts in Mathematics). — ISBN 978-1-4419-3085-9.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.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 Stabilizers
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