Groups, Geometry, and Dynamics


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Volume 4, Issue 3, 2010, pp. 597–603
DOI: 10.4171/GGD/96

Published online: 2010-06-16

Special groups with an elementary hierarchy are virtually free-by-ℤ

Mark F. Hagen[1] and Daniel T. Wise[2]

(1) University of Cambridge, UK
(2) McGill University, Montreal, Canada

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.

Keywords: Free-by-cyclic groups, limit groups, right-angled Artin groups, hierarchies

Hagen Mark, Wise Daniel: Special groups with an elementary hierarchy are virtually free-by-ℤ. Groups Geom. Dyn. 4 (2010), 597-603. doi: 10.4171/GGD/96