Groups and Symmetry

Name: Groups and Symmetry
Author: Mark Armstrong

Gebonden Engels 1997 1e druk 9780387966755

60,94

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Samenvatting

Groups are important because they measure symmetry.

This text, designed for undergraduate mathematics students, provides 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.

Throughout the book, emphasis is placed on concrete examples, often geometrical in nature, so that finite rotation groups and the 17 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 groups actions on trees. There are more than 300 exercises and approximately 60 illustrations to help develop the student's intuition.

Specificaties

ISBN13:9780387966755

Taal:Engels

Bindwijze:gebonden

Aantal pagina's:187

Uitgever:Springer

Druk:1

Verschijningsdatum:27-2-1997

Hoofdrubriek:Wetenschap en techniek

Serie:Undergraduate Texts in Mathematics

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Inhoudsopgave

Preface.

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.
9: Matrix Groups.
10: Products.
: Lagrange's Theorem.
12: Partitions.
13: Cauchy's Theorem.
14: Conjugacy.
15: Quotient Groups.
16: Homomorphisms.
17: Actions, Orbits, and Stabalizers.
18: Counting Orbits.
19: Finite Rotation 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.

Bibliography.
Index.