Bounded group actions on trees and hyperbolic and Lyndon length functions
type: Item
instance of: scholarly article
title: Bounded group actions on trees and hyperbolic and Lyndon length functions
zbMATH Open document ID: 0692.20017
author: David L. Wilkens
published in: Michigan Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let the group G act as a group of isometries on a metric tree T and let K be a normal subgroup with bounded action (that is the distance of any point to any of its K-images is bounded). The action of G gives a hyperbolic length function on G. It is shown that the hyperbolic length function on G is determined by that on G/K and that the Lyndon length functions on G are characterized up to equivalences by those on G/K. Moreover, normal subgroups with bounded action are associated to a length function and there is a maximal normal subgroup with bounded action. Finally, if not every element of G has a fixed point then, for K maximal, G/K is isomorphic to a subgroup of the additive reals or has trivial centre.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 4132427
zbMATH Keywords: group of isometries
zbMATH Keywords: metric tree
zbMATH Keywords: hyperbolic length function
zbMATH Keywords: Lyndon length functions
zbMATH Keywords: normal subgroups with bounded action
zbMATH Keywords: maximal normal subgroup
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003951
OpenAlex ID: W2039523387
DOI: 10.1307/MMJ/1029003951
description: scientific article; zbMATH DE number 4132427