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

Mark Hagen | Zendy; Daniel T. Wise | Zendy

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

Author(s) -

Mark Hagen,

Daniel T. Wise

Publication year - 2010

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/96

Subject(s) - mathematics , hierarchy , free product , free group , group (periodic table) , cyclic group , enhanced data rates for gsm evolution , combinatorics , hyperbolic group , word (group theory) , pure mathematics , hyperbolic manifold , geometry , hyperbolic function , artificial intelligence , computer science , chemistry , abelian group , organic chemistry , economics , market economy

LetG 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.

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