Structure of large incomplete sets in abelian groups

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

What is the structure of a large incomplete set?

We show that such a set is essentially contained in a maximal subgroup. As a co-product, we obtain a new proof for several earlier results, including a new proof for Diderrich’s conjecture in large groups.

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Correspondence to H. Van Vu.

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The author is supported by NSF grant DMS-0901216 and by DoD grant AFOSARFA-9550-09-1-0167.

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Van Vu, H. Structure of large incomplete sets in abelian groups. Combinatorica 30, 225–237 (2010). https://doi.org/10.1007/s00493-010-2336-2

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Mathematics Subject Classification (2000)

  • 11P70
  • 05D99