Geodesic
Special groups with an elementary hierarchy are virtually free-by-$ℤ$
Mark F. Hagen1 orcid ; Daniel T. Wise2
1University of Cambridge, UK
2McGill University, Montreal, Canada
Groups, geometry, and dynamics, Tome 4 (2010) no. 3, pp. 597-603

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DOI

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.
DOI : 10.4171/ggd/96
Classification : 20-XX, 00-XX
Mots-clés : Free-by-cyclic groups, limit groups, right-angled Artin groups, hierarchies

Mark F. Hagen  1   ; Daniel T. Wise  2

1 University of Cambridge, UK
2 McGill University, Montreal, Canada 
Mark F. Hagen; Daniel T. Wise. Special groups with an elementary hierarchy are virtually free-by-$ℤ$. Groups, geometry, and dynamics, Tome 4 (2010) no. 3, pp. 597-603. doi: 10.4171/ggd/96
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