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Acylindrical Hyperbolicity, non-simplicity and SQ-universality of groups splitting over $\mathbb{Z}$
(De GruyterJournal of Group Theory, 2016-09-15)
We show, using acylindrical hyperbolicity, that a finitely generated group splitting over $\mathbb{Z}$ cannot be simple. We also obtain SQ-universality in most cases, for instance a balanced group (one where if two powers ...
Nonhyperbolic free-by-cyclic and one-relator groups
(New York Journal of MathematicsNew York Journal of Mathematicshttp://nyjm.albany.edu/j/2016/22-35.html, 2016-08-01)
We show that the free-by-cyclic groups of the form $F_2$ $\rtimes$ $\Bbb Z$ act properly cocompactly on CAT(0) square complexes. We also show using generalized Baumslag–Solitar groups that all known groups defined by a ...