Result: Minimum sum covers of small cyclic groups

Title:
Minimum sum covers of small cyclic groups
Authors:
Fitch, Mark A., Jamison, Robert E.
Publisher Information:
Combinatorial Press, Winnipeg, MB
Subject Terms:
set addition, Finite abelian groups, finite cyclic groups, Arithmetic progressions, additive bases, sum sets, Arithmetic and combinatorial problems involving abstract finite groups
Document Type:
Academic journal Article
File Description:
application/xml
Access URL:
https://zbmath.org/1599238
Accession Number:
edsair.c2b0b933574d..4ddc0e31b69fbf43729630ab9710fbcb
Database:
OpenAIRE

Further Information

Let \(G\) be a cyclic group of order \(\leq 54\). The authors investigate the structure of minimum subsets \(A\) of \(G\) such that \(2A=G\) (resp. \(A^2=G\)). The first question is related to the famous Rohrbach problem considered by several authors. Let \(H\) be a finite group of order \(n\). \textit{H. Rohrbach} [Math. Z. 42, 538-542 (1937; Zbl 0016.15602)] asked if there exists always a subset \(A\) with size \(c\sqrt n\) such that \(A^2=H\). This statement is now proved [cf. \textit{M. Herzog}, in J.-M. Deshouillers (ed.) et al. Structure theory of set addition. Paris: Société Mathématique de France, Astérisque 258, 309-315 (1999; Zbl 0944.20019)].