Block-transitive, point-imprimitive designs with \(\lambda \Relbar 1\)
type: Item
instance of: scholarly article
title: Block-transitive, point-imprimitive designs with \(\lambda \Relbar 1\)
zbMATH Open document ID: 0777.05015
DOI: 10.1016/0012-365X(93)90492-C
author: Christine M. O'Keefe
author: Tim Penttila
author: Cheryl E. Praeger
published in: Discrete Mathematics
publication date: 1993-06-20T00:00:00Z
review text: Let \(D\) be a 2-\((v,k,1)\) design with a block-transitive group \(G\) of automorphisms transitive and imprimitive on points. Suppose that each block of \(D\) contains exactly one pair of points of the same class. If the subgroup of elements of \(G\) fixing (setwise) each imprimitivity class is not trivial it is elementary abelian of odd order (and transitive on each imprimitivity class) or isomorphic to \(S_ 3\) (and then \(D\) is PG(2,4)). If \(v\) is maximal (i.e. \(v=(k(k-1)/2-1)^ 2\), according to a recent result) then \(v=729\) and \(k=8\), and \(G\) is a product of a point- regular group \(N\) and a group \(H\) of order 13 or 39. There exist 467 pairwise nonisomorphic designs of this type, according to some remarks and a machine enumeration described in a previous paper.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 205604
zbMATH Keywords: automorphisms of BIB-designs
Wikidata QID: Q56988315
reviewed by: Giovanni Ferrero
MaRDI profile type: Publication
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full work available at URL: 0012-365x(93)90492-c
OpenAlex ID: W62547638
DBLP publication ID: journals/dm/OKeefePP93
description: scientific article; zbMATH DE number 205604