On automorphism groups of divisible designs: II: Group invariant generalized conference matrices
type: Item
instance of: scholarly article
title: On automorphism groups of divisible designs: II: Group invariant generalized conference matrices
zbMATH Open document ID: 0659.05030
DOI: 10.1007/BF01198118
author: Dieter Jungnickel
published in: Archiv der Mathematik
publication date: 1990-01-01T00:00:00Z
review text: We prove the non-existence of conference matrices which are invariant under a regular Abelian group. In the non-Abelian case, a group invariant conference matrix of order \(2\lambda +2\) can only exist if \(2\lambda +1\) is a perfect square; no examples of this situation are known, however. These results are applied to obtain non-existence theorems for group invariant generalized conference matrices and thus for splitting relative difference sets. In particular, no splitting Abelian affine difference set of odd order s can exist; for \(s\equiv 3\) mod 4, the non-Abelian case is likewise impossible.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05B10
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 4077236
zbMATH Keywords: balanced weighing matrix
zbMATH Keywords: conference matrices
zbMATH Keywords: generalized conference matrices
zbMATH Keywords: relative difference sets
zbMATH Keywords: affine difference set
MaRDI profile type: Publication
cites work: Affine difference sets of even order
cites work: Q5842118
cites work: Rational G-matrices with rational eigenvalues
cites work: Q3323969
cites work: Solvability of groups of odd order
cites work: Orthogonal Matrices with Zero Diagonal
cites work: Cyclic Affine Planes
cites work: Multiplier theorems
cites work: Intersection theorems for group divisible difference sets
cites work: An affine analogue of Wilbrink's theorem
cites work: Some Aspects of Weighing Designs
cites work: Q5512231
description: scientific article; zbMATH DE number 4077236