Acylindrical hyperbolicity, non simplicity and SQ-universality of groups splitting over Z
Group Theory
2016-03-21 v1
Abstract
We show, using acylindrical hyperbolicity, that a finitely generated group splitting over cannot be simple. We also obtain SQ-universality in most cases, for instance a balanced group (one where if two powers of an infinite order element are conjugate then they are equal or inverse) which is finitely generated and splits over must either be SQ-universal or it is one of exactly seven virtually abelian exceptions.
Keywords
Cite
@article{arxiv.1603.05909,
title = {Acylindrical hyperbolicity, non simplicity and SQ-universality of groups splitting over Z},
author = {J. O. Button},
journal= {arXiv preprint arXiv:1603.05909},
year = {2016}
}
Comments
Much shorter version of 1509.05688 with strengthening of main result