A splitting theorem for groups acting on quasi-trees
Batty, Michael
Batty, Michael
Citation
Batty, Michael (2000). A splitting theorem for groups acting on quasi-trees. Communications in Algebra 28 (2), 967-980
Abstract
It is well known that a group is free if and only if it acts freely without inversions on a tree. We prove a generalisation of this fact by defining a quasi-tree to be a graph with a bound on the size of its simple loops. It is shown that a finitely generated group acting freely on such a graph is isomorphic to a free product of free groups and finite groups.
Funder
Publisher
Informa UK Limited
Publisher DOI
10.1080/00927870008826873
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland