A characterisation of virtually free groups
نویسندگان
چکیده
منابع مشابه
A Characterisation of Virtually Free Groups
We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.
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Let (G, μ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε > 0 such that the Furstenberg entropy of any (G, μ)-stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have property (T). For these groups, we construct stationary actions with arbitrarily small, positive entropy. This co...
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We show that the class of finitely generated virtually free groups is precisely the class of demonstrable subgroups for R. Thompson’s group V . The class of demonstrable groups for V consists of all groups which can embed into V with a natural dynamical behaviour in their induced actions on the Cantor space C2 := {0, 1}. There are also connections with formal language theory, as the class of gr...
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A fixed point theorem is proved for inverse transducers, leading to an automatatheoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regular fixed points in the hyperbolic boundary has finitely many orbits under the a...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2007
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-007-2206-3