Result: The Erdős-Heilbronn problem in Abelian groups: The Erdős-Heilbronn problem in Abelian groups.

Title:
The Erdős-Heilbronn problem in Abelian groups: The Erdős-Heilbronn problem in Abelian groups.
Authors:
Karolyi, G.
Source:
Israel Journal of Mathematics. 139:349-359
Publisher Information:
Springer Science and Business Media LLC, 2004.
Publication Year:
2004
Subject Terms:
Congruence classes, addition theorems, 4. Education, Other combinatorial number theory, Special sequences and polynomials, Spaces, Restricted sums, 0102 computer and information sciences, 0101 mathematics, 16. Peace & justice, inverse additive theorems, 01 natural sciences, Arithmetic and combinatorial problems involving abstract finite groups
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1565-8511
0021-2172
DOI:
10.1007/bf02787556
Access URL:
https://zbmath.org/2114536
https://doi.org/10.1007/bf02787556
https://link.springer.com/content/pdf/10.1007/BF02787556.pdf
https://espace.library.uq.edu.au/view/UQ:269339
https://link.springer.com/article/10.1007/BF02787556
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....2e2babde8dcaff30540e4ffde9bf0dcc
Database:
OpenAIRE

Further Information

Let \(X\) be a subset of an abelian group. We denote by \(2\wedge X\) the set of sums of two distinct elements of \(X\). Let \(A\) be a finite subset of an abelian group \(G\) and let \(p\) denote the smallest cardinality of a subgroup of \(G\). The author proves that \(|2\wedge A|\geq 2|A|-3\). If \(|G|\) is prime, this result reduces to theorem proved first by \textit{J. A. Dias da Silva} and the reviewer [Bull. Lond. Math. Soc. 26, 140-146 (1994; Zbl 0819.11007)].