On homogeneous semilattices and their automorphism groups
type: Item
instance of: scholarly article
title: On homogeneous semilattices and their automorphism groups
zbMATH Open document ID: 0945.06001
DOI: 10.1023/A:1006365012997
author: Dietrich Kuske
author: Manfred Droste
author: John K. Truss
published in: Order
publication date: 2000-10-08T00:00:00Z
review text: A semilattice \((S,\lor)\) is called homogeneous if each isomorphism between two finite subsemilattices of \(S\) extends to an automorphism of \(S\). It is shown that there are just countably many countable homogeneous semilattices. A semilattice \((S,\lor)\) is said to be universal if each countable semilattice embeds into it. It is proved that the automorphism group of the universal homogeneous countable semilattice has a largest proper nontrivial normal subgroup.
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 20B27
zbMATH DE Number: 1423852
zbMATH Keywords: homogeneous semilattices
zbMATH Keywords: automorphism group
zbMATH Keywords: normal subgroup
reviewed by: V. N. Saliĭ
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1423852