Simulated factorizations. II
type: Item
instance of: scholarly article
title: Simulated factorizations. II
zbMATH Open document ID: 0795.20039
DOI: 10.1007/BF01834204
published in: Aequationes Mathematicae
publication date: 1993-01-06T00:00:00Z
full work available at URL: https://eudml.org/doc/137479
review text: A factorization of a finite abelian group is said to be simulated if it is obtained from a factorization into a direct product of subgroups by changing at most \(k\) elements in each subgroup. The question has been asked which values of \(k\) imply that in fact at least one subgroup must be left unaltered. This has been shown to be true for \(k=1\) but to be false, in general, for \(k=p-1\), where \(p\) is the least prime dividing the order of \(G\) [see part I, \textit{K. Corrádi}, \textit{A. D. Sands} and \textit{S. Szabó}, J. Algebra 151, No. 1, 12-25 (1992; Zbl 0774.20030)]. In the paper reviewed, it is shown to be true for \(k=p-2\). This result is stated as Theorem 5. Let \(G\) be a direct product of subsets \(A_ 1,\dots, A_ n\) and let there exist subgroups \(H_ 1,\dots, H_ n\) such that \(| A_ i|= | H_ i|\) and \(| A_ i|\leq | A_ i\cap H_ i|+p-2\), where \(p\) is the least prime factor of \(| G|\). Then there exists an \(i\) such that \(A_ i= H_ i\).
reviewed by: Yongcai Ren
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 52C22
zbMATH DE Number: 85813
zbMATH Keywords: factorization
zbMATH Keywords: finite abelian group
zbMATH Keywords: direct product of subgroups
zbMATH Keywords: direct product of subsets
zbMATH Keywords: subgroups
Wikidata QID: Q114233919
author: A. Sands
MaRDI profile type: Publication
cites work: A new proof of Rédei's theorem
cites work: Q5818512
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description: scientific article; zbMATH DE number 85813