Structure of large incomplete sets in abelian groups

Details Structure of large incomplete sets in abelian groups Structure of large incomplete sets in abelian groups

2006-10-04

arxiv.org/abs/math/0610158v1

Mathematics

Combinatorics

Scientific paper

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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