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