Translation nets and fixed-point-free group automorphisms
type: Item
instance of: scholarly article
title: Translation nets and fixed-point-free group automorphisms
zbMATH Open document ID: 0716.05007
DOI: 10.1016/0097-3165(90)90043-V
author: R. A. Bailey
author: Dieter Jungnickel
published in: Journal of Combinatorial Theory. Series A
publication date: 1990-01-01T00:00:00Z
review text: The authors discuss the equivalence of three mathematical objects: translation nets (i.e. nets with a regular automorphism group which preserves parallel classes), sets of MOLS with a regular group of strong automorphisms, and partial congruence partitions of a group (i.e. sets of subgroups of the same order \(n\), if \(n^ 2\) is the order of the group, such that any two subgroups have a trivial intersection). They review known results (and give good references), provide a construction which shows the equivalence above, with the help of a fixed- point-free set of automorphism of a group. Bounds are proven for the maximum size of a set of MOLS. In the special case of an abelian p-group H, the exact values are given for the maximum size of a set of MOLS based on \(H\) (and constructed by Mann's automorphism method), for the number of parallel classes of a translation net (with \(H\times H\) as a translation group) and for the maximal degree (number of subgroups) of a partial congruence partition of \(H\times H\). Improvements are also provided of the known bounds for non-abelian \(p\)-groups. Some applications are shown to partial difference sets, strongly regular graphs and design of experiments.
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 4179386
zbMATH Keywords: partial congruence partitions of groups
zbMATH Keywords: translation nets
zbMATH Keywords: MOLS
MaRDI profile type: Publication
cites work: A Unified Approach to Design of Experiments
cites work: Q3960862
cites work: Q3737429
cites work: On Methods of Constructing Sets of Mutually Orthogonal Latin Squares Using a Computer. I
cites work: Q3885786
cites work: Q3863891
cites work: Optimality of some two-associate-class partially balanced incomplete- block designs
cites work: Q3241542
cites work: Q4769064
cites work: Q4115154
cites work: The Logic of Inductive Inference
cites work: Groups with a large number of large disjoint subgroups
cites work: Hadamard difference sets in groups of order 64
cites work: Q5577154
cites work: Q5802543
cites work: Orthomorphisms of Groups and Orthogonal Latin Squares. I
cites work: Q3905299
cites work: Partial spreads over \({\mathbb{Z}}_ q\)
cites work: Partial difference sets
cites work: The Construction of Orthogonal Latin Squares
cites work: THE 7 × 7 SQUARES
cites work: Q3965191
description: scientific article; zbMATH DE number 4179386