TY  - BOOK
AU  - Armstrong, Mark A.
ED  - SpringerLink (Online service)
TI  - Groups and Symmetry
T2  - Undergraduate Texts in Mathematics,
SN  - 9781475740349
AV  - QA174-183 
U1  - 512.2 23
PY  - 1988///
CY  - New York, NY
PB  - Springer New York, Imprint: Springer
KW  - Group theory
KW  - Group Theory and Generalizations
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-1-4757-4034-9
ER  -