A Hajós-Keller type result on factorization of finite cyclic groups
type: Item
instance of: scholarly article
title: A Hajós-Keller type result on factorization of finite cyclic groups
zbMATH Open document ID: 0728.20044
DOI: 10.1007/BF01950939
author: Sándor Szabó
author: K. Corrádi
published in: Acta Mathematica Hungarica
publication date: 1990-01-01T00:00:00Z
review text: Let G be a finite Abelian group, let \(g\in G\) and denote by [g,q] the simplex \(\{\) 0,g,2g,...,(q-1)g\(\}\), where \(1\leq q\leq | g|\). A normed factorization of G is an equality of the form \(G=A_ 1+A_ 2+...+A_ n\), where \(0\in A_ i\subset G\), \(1\leq i\leq n.\) Using Hajos' theorem, the authors prove the following result which is related to a conjecture of Keller [cf. \textit{S. K. Stein}, Am. Math. Mon. 81, 445-462 (1974; Zbl 0284.20048)]: If \(G=H+[g_ 1,q_ 1]+...+[g_ n,q_ n]\) is a normed factorization of the finite cyclic group G, then there exists some j, \(1\leq j\leq n\) such that \(q_ jg_ j\in <H>\).
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 11H31
zbMATH DE Number: 4202587
zbMATH Keywords: finite Abelian group
zbMATH Keywords: simplex
zbMATH Keywords: normed factorization
zbMATH Keywords: Hajos' theorem
zbMATH Keywords: finite cyclic group
reviewed by: Marian Deaconescu
MaRDI profile type: Publication
cites work: Über einfache und mehrfache Bedeckung des \(n\)-dimensionalen Raumes mit einem Würfelgitter
cites work: Die neue Theorie der endlichen abelschen Gruppen und Verallgemeinerung des Hauptsatzes von Hajós
cites work: Algebraic Tiling
full work available at URL: https://doi.org/10.1007/bf01950939
OpenAlex ID: W2010698179
description: scientific article; zbMATH DE number 4202587