Partial difference sets in \(p\)-groups

DOI10.1007/BF01189882zbMath0811.05012OpenAlexW2085015355MaRDI QIDQ1337784

James A. Davis

Publication date: 13 November 1994

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01189882

zbMATH Keywords

partial difference setselementary abelian \(p\)-groupsnonelementary abelian groupPaley parametersreversible divisible difference sets

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Finite abelian groups (20K01) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10)

Related Items (17)

Packings of partial difference sets ⋮ Negative Latin square type partial difference sets and amorphic association schemes with Galois rings ⋮ A new family of partial difference sets in 3-groups ⋮ Partial difference sets and amorphic group schemes from pseudo-quadratic bent functions ⋮ Edge connectivity in difference graphs and some new constructions of partial sum families ⋮ Paley type partial difference sets in abelian groups ⋮ Abelian and non-abelian Paley type group schemes ⋮ A new product construction for partial difference sets ⋮ Partial sum quadruples and bi-abelian digraphs ⋮ Paley partial difference sets in groups of order \(n^{4}\) and \(9n^{4}\) for any odd \(n>1\) ⋮ A construction of partial difference sets in \(\mathbb{Z}_{p^ 2}\times \mathbb{Z}_{p^ 2}\times\cdots\times \mathbb{Z}_{p^ 2}\) ⋮ Paley type sets from cyclotomic classes and Aarasu-Dillon-Player difference sets ⋮ Paley type group schemes and planar Dembowski-Ostrom polynomials ⋮ Paley type partial difference sets in non \(p\)-groups ⋮ Strong difference families, difference covers, and their applications for relative difference families ⋮ Strongly regular tri-Cayley graphs ⋮ Strongly regular Cayley graphs over the group \({\mathbb Z}_{p^n}\oplus {\mathbb Z}_{p^n}\)

Cites Work

• Partial difference sets
• Divisible difference sets with multiplier -1
• Symmetric divisible designs with \(k-\lambda{}_ 1=1\)
• Abelian divisible difference sets with multiplier \(-1\)
• Strongly regular Cayley graphs with \(\lambda-\mu=-1\)
• Character sums and difference sets
• Constructions of Partial Difference Sets and Relative Difference Sets on p -Groups
• On Orthogonal Matrices

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