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

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.

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.