Groups assembled from free and direct products
type: Item
instance of: scholarly article
title: Groups assembled from free and direct products
zbMATH Open document ID: 0782.05040
DOI: 10.1016/0012-365X(92)90279-O
author: Carl Droms
author: Brigitte Servatius
author: Herman J. Servatius
published in: Discrete Mathematics
publication date: 1993-10-14T00:00:00Z
review text: Let \(A\) be the smallest class of groups which contains the infinite cyclic group \(Z\), and which contains both the free product and the direct product of any two of its members. These groups can be described in several ways by graphs. In this paper the subgroups of \(A\)-groups are examined. A finite graph is called an assembly if it belongs to the smallest collection of graphs containing the one-point graph \(K_ 1\), and which is closed under the operations ``disjoint union'' and ``join''. Let \(A\) be an assembly, and let \(\Gamma\) be a finite graph. If there is a monomorphism \(f: F_ \Gamma\to F_ A\), then \(\Gamma\) is an assembly. Let \(A\) and \(A'\) be finite assemblies and let \(f: F_{A'}\to F_ A\) be a monomorphism. Then \(A'\leq A\).
reviewed by: Ulrike Baumann
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 428127
zbMATH Keywords: free product
zbMATH Keywords: direct product
zbMATH Keywords: assembly
zbMATH Keywords: finite graph
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 428127