Szabo / Sands Factoring Groups into Subsets

1. Auflage 2010
ISBN: 978-1-4200-9047-5
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 274 Seiten

Reihe: Lecture Notes in Pure and Applied Mathematics

Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups.

The book first shows how to construct new factorizations from old ones. The authors then discuss nonperiodic and periodic factorizations, quasiperiodicity, and the factoring of periodic subsets. They also examine how tiling plays an important role in number theory. The next several chapters cover factorizations of infinite abelian groups; combinatorics, such as Ramsey numbers, Latin squares, and complex Hadamard matrices; and connections with codes, including variable length codes, error correcting codes, and integer codes. The final chapter deals with several classical problems of Fuchs.

Encompassing many of the main areas of the factorization theory, this book explores problems in which the underlying factored group is cyclic.

Zielgruppe

Graduate students and researchers in mathematics.

Autoren/Hrsg.

Szabo, Sandor

Sands, Arthur D.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

Introduction
New Factorizations from Old Ones
Restriction
Factorization
Homomorphism
Constructions
Nonperiodic Factorizations
Bad factorizations
Characters
Replacement
Periodic Factorizations
Good factorizations
Good groups
Krasner factorizations
Various Factorizations
The Rédei property
Quasiperiodicity
Factoring by Many Factors
Factoring periodic subsets
Simulated subsets
Group of Integers
Sum sets of integers
Direct factor subsets
Tiling the integers
Infinite Groups
Cyclic subgroups
Special p-components
Combinatorics
Complete maps
Ramsey numbers
Near factorizations
A family of random graphs
Complex Hadamard matrices
Codes
Variable length codes
Error correcting codes
Tilings
Integer codes
Some Classical Problems
Fuchs’s problems
Full-rank factorizations
Z-subsets
References
Index