Automorphism groups of countable highly homogeneous partially ordered sets
type: Item
instance of: scholarly article
title: Automorphism groups of countable highly homogeneous partially ordered sets
zbMATH Open document ID: 0792.20002
DOI: 10.1007/BF02572390
author: A. M. W. Glass
author: Stephen H. McCleary
author: Matatyahu Rubin
published in: Mathematische Zeitschrift
publication date: 1994-07-21T00:00:00Z
full work available at URL: https://eudml.org/doc/174554
review text: We prove Theorem 1. The automorphism group \(G\) of the countable universal poset is simple. Actually, if \(g\in G\) and \(g \neq 1\), then every element of \(G\) can be written in the form \(\prod^ 8_{j = 1}(h^{-1}_{2j-1} gh_{2j-1} \cdot h^{-1}_{2j} g^{-1} h_{2j})\), for some \(h_ 1,\dots,h_{16} \in G\). Theorem 2. If \((\Omega,\leq)\) is a countable highly homogeneous poset, then ``almost all'' finitely generated subgroups of \(\text{Aut}(\Omega,\leq)\) are free. (``Almost all'' is in the Baire Category sense).
reviewed by: A. M. W. Glass
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E32
Mathematics Subject Classification ID: 20B22
zbMATH DE Number: 561285
zbMATH Keywords: automorphism group
zbMATH Keywords: countable universal poset
zbMATH Keywords: highly homogeneous poset
zbMATH Keywords: finitely generated subgroups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 561285