ABSTRACT

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. Th

Introduction. New Factorizations from Old Ones. Nonperiodic Factorizations. Periodic Factorizations. Various Factorizations. Factoring by Many Factors. Group of Integers. Infinite Groups. Combinatorics. Codes. Some Classical Problems. References. Index.