Structure of large incomplete sets in abelian groups

2006/10/04 by Van H. Vu, Vu, Van H.
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.math/0610158

arxiv created 2006/10/04 · arxiv updated 2009/12/01

Abstract

Let G be a finite abelian group and A be a subset of G. We say that A is complete if every element of G can be represented as a sum of different elements of A. In this paper, we study the following question: \it What is the structure of a large incomplete set ? The typical answer is that such a set is essentially contained in a maximal subgroup. As a by-product, we obtain a new proof for several earlier results.

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