Let G be a group with a hierarchy whose edge groups at each level are cyclic. We show that when G is also word-hyperbolic, then G is virtually free-by-cyclic. In particular, this holds for groups splitting as graphs of free groups with cyclic edge groups unless they have Baumslag–Solitar subgroups that are not virtually products.
Cite this article
Mark F. Hagen, Daniel T. Wise, Special groups with an elementary hierarchy are virtually free-by-ℤ. Groups Geom. Dyn. 4 (2010), no. 3, pp. 597–603DOI 10.4171/GGD/96