\(t\)-divisible designs from imprimitive permutation groups
type: Item
instance of: scholarly article
title: \(t\)-divisible designs from imprimitive permutation groups
zbMATH Open document ID: 0767.05020
DOI: 10.1016/S0195-6698(05)80020-4
author: Antonino Giorgio Spera
published in: European Journal of Combinatorics
publication date: 1993-01-16T00:00:00Z
review text: A \(t\)-divisible design \((t\)-DD) is known as a group divisible design if \(t=2\) and the size of a point class exceeds 1, and a \(t\)-DD is simply a \(t\)-design if a point class is of size 1. The author constructs \(t\)-DD's by means of \(R\)-permutation groups \((G,X,R)\), where \(R\) is an equivalence relation on the set \(X\) and \(G\) is an \(R\)-admissable permutation group on \(X\) that is \(t\)-\(R\)-transitive. He also introduces the idea of a transitive extension of such a group and links it with the extension of a \(t\)-DD. The 2-DD's and 3-DD's obtained by extensions of certain classical groups are classified as well.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 20B99
zbMATH DE Number: 94943
zbMATH Keywords: \(t\)-divisible design
zbMATH Keywords: permutation group
zbMATH Keywords: transitive extension
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
cites work: Q3753017
cites work: Tits's theorem for the group \(PGL_ 2(L)\), L a not necessarily commutative local ring
cites work: Q3686719
cites work: On the foundations of polar geometry. II
cites work: A class of three-designs
cites work: Extended partial geometries: Nets and dual nets
cites work: Q5721209
cites work: On t-Designs and Groups
cites work: Q5184922
cites work: Q4046212
full work available at URL: s0195-6698(05)80020-4
OpenAlex ID: W2030176008
description: scientific article; zbMATH DE number 94943