Nonabelian sets with distinct \(k\)-sums
type: Item
instance of: scholarly article
title: Nonabelian sets with distinct \(k\)-sums
zbMATH Open document ID: 0837.05023
DOI: 10.1016/0012-365X(94)00162-7
author: Yanyan Li
published in: Discrete Mathematics
publication date: 1995-12-12T00:00:00Z
review text: A subset \(S\) of a finite abelian group \(G\) is called an \(S_k\)-set provided that all sums of \(k\) elements selected from \(S\) are distinct. In the special case \(k = 2\), this condition is equivalent to the requirement that all nonzero differences \(d - e\) with \(d,e \in S\) are distinct; thus planar difference sets provide examples, and finding large \(S_2\)-sets may be viewed as a sort of packing problem for difference sets. In view of the multiplier theory for difference sets, one might ask whether there are \(S_k\)-sets admitting ``multipliers''. As the authors show by modifying a construction of Bose and Chowla, the answer to this question is positive: For every integer \(k \geq 2\) and every prime \(p \equiv 1 \pmod k\), there exists an \(S_k\)-set \(S\) of cardinality \(p\) in \(Z_m\), where \(m = p^k - 1\), such that \(S = pS\). The authors also consider a nonabelian version of \(S_k\)-sets and construct large sets \(S\) in certain nonabelian groups such that all \(k\)-letter words with letters from \(S\) are distinct.
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 825351
zbMATH Keywords: \(k\)-sums
zbMATH Keywords: difference sets
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
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full work available at URL: 0012-365x(94)00162-7
OpenAlex ID: W2010016765
description: scientific article; zbMATH DE number 825351