On divisible difference sets which are fixed by the inverse
type: Item
instance of: scholarly article
title: On divisible difference sets which are fixed by the inverse
zbMATH Open document ID: 0685.05008
DOI: 10.1007/BF01189590
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: Let G be a finite group of order mn with a subgroup N of order n. A k- element subset D of G is called an \((m,n,k,\lambda_ 1,\lambda_ 2)\)- divisible difference set if the expressions \(d_ 1d_ 2^{-1}\), for \(d_ 1\) and \(d_ 2\) in D with \(d_ 1\neq d_ 2\), represent each element in \(G\setminus N\) exactly \(\lambda_ 2\) times and each element in \(N\setminus \{e\}\) exactly \(\lambda_ 1\) times. In this paper, we study the particular case that D is fixed by the inverse, that is, \(D^{(-1)}=\{g^{-1}| g\in D\}=D\). Existence and nonexistence results will be given.
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 4122005
zbMATH Keywords: divisible difference set
author: Siu Lun Ma
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01189590
OpenAlex ID: W2017838331
description: scientific article; zbMATH DE number 4122005