The normal subgroup lattice of 2-transitive automorphism groups of linearly ordered sets
type: Item
instance of: scholarly article
title: The normal subgroup lattice of 2-transitive automorphism groups of linearly ordered sets
zbMATH Open document ID: 0583.06001
author: Manfred Droste
published in: Order
publication date: 1985-01-01T00:00:00Z
review text: An infinite linearly ordered set, or briefly infinite chain, (\(\Omega\),\(\leq)\) is called doubly homogeneous if its automorphism group A(\(\Omega)\) acts 2-transitively on the set \(\Omega\). The author investigates the lattice N(A(\(\Omega)\)) of all normal subgroups of A(\(\Omega)\) using combinatorial and model-theoretic means. Certain natural sublattices of N(A(\(\Omega)\)) are shown to be Stone algebras, and several first order properties of their dense and dually dense elements are characterized within the Dedekind-completion of (\(\Omega\),\(\leq)\). As consequences, various group- and lattice-theoretic results follow from this.
reviewed by: J.Libicher
Mathematics Subject Classification ID: 06A05
Mathematics Subject Classification ID: 20B27
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 03C20
zbMATH DE Number: 3933130
zbMATH Keywords: lattice of normal subgroups
zbMATH Keywords: infinite linearly ordered set
zbMATH Keywords: doubly homogeneous
zbMATH Keywords: automorphism group
zbMATH Keywords: 2-transitively
zbMATH Keywords: first order properties
zbMATH Keywords: dually dense elements
zbMATH Keywords: Dedekind-completion
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3933130