Groups and Symmetry

1. Auflage 1988. Corr. 2. printing. Softcover version of original hardcover Auflage 1988
ISBN: 978-1-4419-3085-9
Verlag: Springer

Buch, Englisch, 187 Seiten, Previously published in hardcover, Format (B × H): 156 mm x 234 mm, Gewicht: 319 g

Reihe: Undergraduate Texts in Mathematics

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Armstrong, Mark A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.- 10 Products.- 11 Lagrange’s Theorem.- 12 Partitions.- 13 Cauchy’s Theorem.- 14 Conjugacy.- 15 Quotient Groups.- 16 Homomorphisms.- 17 Actions, Orbits, and Stabilizers.- 18 Counting Orbits.- 19 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.