English

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 xmx^m conjugate to xnx^n implies that m=n|m|=|n| for all infinite order elements xx.

Keywords

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}
}
R2 v1 2026-06-22T10:59:59.147Z