Partial difference sets in \(p\)-groups
type: Item
instance of: scholarly article
title: Partial difference sets in \(p\)-groups
zbMATH Open document ID: 0811.05012
DOI: 10.1007/BF01189882
author: James A. Davis
published in: Archiv der Mathematik
publication date: 1994-11-13T00:00:00Z
review text: Partial difference sets (PDSs) have been constructed in elementary abelian \(p\)-groups. Several authors have inquired about the existence of PDSs with the same parameters in other (non-elementary) abelian \(p\)- groups. This paper provides an exponent bound for PDSs in abelian \(p\)- groups for the Paley parameters. We also provide the first construction of a PDS with the Paley parameters in a nonelementary abelian group. We note the implications to reversible divisible difference sets.
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 687050
zbMATH Keywords: partial difference sets
zbMATH Keywords: elementary abelian \(p\)-groups
zbMATH Keywords: Paley parameters
zbMATH Keywords: nonelementary abelian group
zbMATH Keywords: reversible divisible difference sets
MaRDI profile type: Publication
cites work: Divisible difference sets with multiplier -1
cites work: Symmetric divisible designs with \(k-\lambda{}_ 1=1\)
cites work: Strongly regular Cayley graphs with \(\lambda-\mu=-1\)
cites work: Abelian divisible difference sets with multiplier \(-1\)
cites work: Constructions of Partial Difference Sets and Relative Difference Sets on p -Groups
cites work: Partial difference sets
cites work: On Orthogonal Matrices
cites work: Character sums and difference sets
full work available at URL: https://doi.org/10.1007/bf01189882
OpenAlex ID: W2085015355
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description: scientific article; zbMATH DE number 687050