Year: 2015
Type: preprint
Abstract: We give a necessary and sufficient condition for the fundamental group of a finite graph of groups with infinite cyclic edge groups to be acylindrically hyperbolic, from which it follows that a finitely generated group splitting over Z cannot be simple. We also give a necessary and sufficient condition (when the vertex groups are torsion free) for the fundamental group to be balanced, where a group is said to be balanced if $x^m$ conjugate to $x^n$ implies that $|m|=|n|$ for all infinite order elements $x$.
Source: arXiv (Cornell University)
Author: Button, J. O.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2227710873