Subgroups of free metabelian groups.
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.
intersections of finitely generated subgroups
scientific article; zbMATH DE number 5880957
scientific article