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Catalogue Information
Field name
Details
Dewey Class
512.2
Title
Groups and Symmetry ([EBook]) / by M. A. Armstrong.
Author
Armstrong, Mark Anthony
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : Springer , 1988.
Physical Details
XI, 187 pages : online resource.
Series
Undergraduate texts in mathematics
0172-6056
ISBN
9781475740349
Summary Note
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.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4757-4034-9
Links to Related Works
Subject References:
Group theory
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Group Theory and Generalizations
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Mathematics
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Authors:
Armstrong, Mark Anthony
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Corporate Authors:
SpringerLink (Online service)
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Series:
Undergraduate texts in mathematics
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Classification:
512.2
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