Cyclic affine planes of even order
type: Item
instance of: scholarly article
title: Cyclic affine planes of even order
zbMATH Open document ID: 0682.05021
DOI: 10.1016/0012-365X(89)90317-8
author: K. T. Arasu
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let a be an integer. If t is any integer with \((t,a)=1\), \(\exp_ a(t)\) would mean the smallest positive integer \(\ell\) such that \(t^{\ell}\equiv 1 (mod a)\). Let (p/q) be the Legendre symbol. The main purpose of the paper is to prove the following result. Suppose that there exists a cyclic affine plane of even order n. Then (1) either \(n=2\) or \(n\equiv 0 (mod 4);\) (2) for each prime divisor p of n, we have either \((p/q)=1\) for each prime q, \(q| n^ 2-1\), and for some positive integer r, \(n+1| p^ r+1\) and \(n-1| p^ r-1\), according as \(\exp_{n^ 2-1}(p)\) is odd or even.
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 4116552
zbMATH Keywords: difference sets
zbMATH Keywords: cyclic affine plane
reviewed by: Giorgio Faina
MaRDI profile type: Publication
cites work: Projectivities of Finite Projective Planes
cites work: Q5842118
cites work: Relative difference sets
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cites work: Generalized incidence matrices over group algebras
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cites work: A note on affine difference sets
cites work: Intersection theorems for group divisible difference sets
cites work: Q3856855
description: scientific article; zbMATH DE number 4116552