Regular completions of ${\mathbb{Z}}^n$-free groups

Abstract

In the present paper we continue studying regular free group actions on ${\mathbb{Z}}^n$-trees. We show that every finitely generated ${\mathbb{Z}}^n$-free group $G$ can be embedded into a finitely generated ${\mathbb{Z}}^n$-free group $H$ acting regularly on the underlying ${\mathbb{Z}}^n$-tree (we call $H$ a {\em regular ${\mathbb{Z}}^n$-completion} of $G$) so that the action of $G$ is preserved. Moreover, if $G$ is effectively represented as a group of ${\mathbb{Z}}^n$-words then the construction of $H$ is effective and $H$ is also effectively represented as a group of ${\mathbb{Z}}^n$-words.

22 pages

References in corpus (2)

• Finite index subgroups of fully residually free groups
• Infinite words and universal free actions