Front cover image for Groups and Symmetry

Groups and Symmetry

Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to 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, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the seventeen 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 group actions on trees. There are more than three hundred exercises and approximately sixty illustrations to help develop the student's intuition
eBook, English, 1988
Springer New York, New York, NY, 1988
1 online resource (xi, 187 pages)
9781475740349, 1475740344
851768121
Print version:
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
Bibliography
Index
English