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MARC 21

Groups and Symmetry
Tag	Description
020	$a9781475740349
082	$a512.2
099	$aOnline resource: Springer
100	$aArmstrong, Mark Anthony
245	$aGroups and Symmetry$h[EBook]$cby M. A. Armstrong.
260	$aNew York, NY$bSpringer$c1988.
300	$aXI, 187 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aUndergraduate Texts in Mathematics,$x0172-6056
505	$a1 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.
520	$aGroups 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aUndergraduate Texts in Mathematics,
856	$uhttp://dx.doi.org/10.1007/978-1-4757-4034-9