An inverse theorem for the restricted set addition in Abelian groups

Karolyi, G (2005) An inverse theorem for the restricted set addition in Abelian groups. Journal of Algebra, 290 2: 557-593. doi:10.1016/j.jalgebra.2005.04.021


Author Karolyi, G
Title An inverse theorem for the restricted set addition in Abelian groups
Journal name Journal of Algebra   Check publisher's open access policy
ISSN 0021-8693
Publication date 2005-08-01
Sub-type Article (original research)
DOI 10.1016/j.jalgebra.2005.04.021
Open Access Status Not Open Access
Volume 290
Issue 2
Start page 557
End page 593
Total pages 37
Place of publication Maryland Heights, MO, United States
Publisher Academic Press
Language eng
Formatted abstract
Let A be a set of k ≥ 5 elements of an Abelian group G in which the order of the smallest nonzero subgroup is larger than 2k - 3. Then the number of different elements of G that can be written in the form a + a′, where a, a′ ∈ A, a ≠ a′, is at least 2k - 3, as it has been shown in [Gy. Károlyi, The Erdos-Heilbronn problem in Abelian groups, Israel J. Math. 139 (2004) 349-359]. Here we prove that the bound is attained if and only if the elements of A form an arithmetic progression in G, thus completing the solution of a problem of Erdos and Heilbronn. The proof is based on the so-called 'Combinatorial Nullstellensatz.'
Keyword Congrujence classes
Small sumsets
Residues
Spaces
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Fri, 02 Mar 2012, 20:48:25 EST by Kay Mackie on behalf of School of Mathematics & Physics