Subgroups of free metabelian groups.
type: Item
instance of: scholarly article
title: Subgroups of free metabelian groups.
zbMATH Open document ID: 1230.20034
DOI: 10.4171/GGD/99
author: Gilbert Baumslag
author: Charles F. III Miller
author: Gretchen Ostheimer
published in: Groups, Geometry, and Dynamics
publication date: 2011-04-21T00:00:00Z
review text: A new way of describing metabelian groups is proposed. The notion of so called hybrid presentation of a metabelian group is introduced in the paper. Every finitely generated metabelian group has a finite hybrid presentation. Interest of the authors in finite hybrid presentations is to use them in investigating the subgroups of given metabelian groups and to help understand how such subgroups intersect. The object of the paper is to explore such intersections in free metabelian groups and more generally, in the wreath product of two free Abelian groups. In such a wreath product it is shown, for instance, that there are algorithms to decide whether or not the intersection of two finitely generated subgroups is finitely generated or trivial.
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 5880957
zbMATH Keywords: free metabelian groups
zbMATH Keywords: wreath products
zbMATH Keywords: intersections of finitely generated subgroups
zbMATH Keywords: Howson property
zbMATH Keywords: algorithms
zbMATH Keywords: finite hybrid presentations
reviewed by: Vitaliĭ Roman'kov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5880957