Balanced groups and graphs of groups with infinite cyclic edge groups
Group Theory
2015-09-21 v1
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 conjugate to implies that for all infinite order elements .
Cite
@article{arxiv.1509.05688,
title = {Balanced groups and graphs of groups with infinite cyclic edge groups},
author = {J. O. Button},
journal= {arXiv preprint arXiv:1509.05688},
year = {2015}
}