\(D\)-set and groups
type: Item
instance of: scholarly article
title: \(D\)-set and groups
zbMATH Open document ID: 0840.20068
DOI: 10.1007/BF00676276
published in: International Journal of Theoretical Physics
publication date: 1996-05-28T00:00:00Z
review text: The author introduces the following two definitions. A nonempty set \(L\) with partial binary operation \(\ominus\) is called a difference set if the following conditions are true: (d1) For any \(a\in L\Rightarrow a\ominus a\in L\), (d2) If \(a,b,a\ominus b\in L\), then \(a\ominus (a\ominus b)=b\), (d3) If \(a,b,c, a\ominus b\), \(b\ominus c\in L\), then \(a\ominus c\in L\) and \((a\ominus c)\ominus (a\ominus b)= b\ominus c\). A difference set \(L\) is called a group difference set if in addition to conditions (d1)--(d3) the following condition is true: (d4) \(a\ominus b\in L\) if and only if \(b\ominus a\in L\). Some properties of (group) difference sets are investigated.
Mathematics Subject Classification ID: 20N02
Mathematics Subject Classification ID: 08A55
Mathematics Subject Classification ID: 20K99
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 844086
zbMATH Keywords: abelian groups
zbMATH Keywords: partial binary operation
zbMATH Keywords: group difference set
zbMATH Keywords: difference sets
author: Ol'ga Nánásiová
reviewed by: S. A. Gurchenkov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 844086