Semilinear tower of Steiner systems
type: Item
instance of: scholarly article
title: Semilinear tower of Steiner systems
zbMATH Open document ID: 0836.05010
DOI: 10.1016/0097-3165(95)90063-2
author: S. A. Adeleke
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-03-26T00:00:00Z
review text: The author considers infinite Steiner systems; more precisely, a Steiner system consists of a set \(\Omega\) of points and countably infinite subsets of \(\Omega\), blocks, such that every pair of points is contained in a unique block. By building a suitable semilinear tower of Steiner systems (i.e. any pair of distinct Steiner systems with two elements in common must have one contained in a single block of the other), the following result is proved: There exists an infinite Jordan group \((G, \Omega)\) such that (i) \((G, \Omega)\) is 3-transitive but not 3-primitive; (ii) \(G\) preserves a limit of Steiner systems on \(\Omega\); (iii) \(G\) preserves none of the following relations on \(\Omega\): linear or circular order, separation relation, relations induced on maximal chains and leaves of a tree; (iv) \(G\) preserves no nontrivial Steiner systems; (v) \(G_\alpha\) preserves a relation on maximal chains on \(\Omega \backslash \{\alpha\}\), \(\alpha \in \Omega\).
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 51E10
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 20B99
zbMATH DE Number: 823495
zbMATH Keywords: infinite Steiner systems
zbMATH Keywords: semilinear tower
zbMATH Keywords: Jordan group
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90063-2
OpenAlex ID: W2073656898
cites work: Q3343210
cites work: Transitivity of permutation groups on unordered sets
cites work: Classification of Infinite Primitive Jordan Permutation Groups
description: scientific article; zbMATH DE number 823495