Geometric characterizations 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.
متن کاملFurstenberg Entropy Realizations for Virtually Free Groups and Lamplighter Groups
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...
متن کاملGeometric Characterizations of Finite Chevalley Groups of Type B2
Finite Moufang generalized quadrangles were classified in 1974 as a corollary to the classification of finite groups with a split BN-pair of rank 2, by P. Fong and G. M. Seitz (1973), (1974). Later on, work of S. E. Payne and J. A. Thas culminated in an almost complete, elementary proof of that classification; see Finite Generalized Quadrangles, 1984. Using slightly more group theory, first W. ...
متن کاملFixed points of endomorphisms of virtually free groups
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...
متن کاملThe Subgroup Growth Spectrum of Virtually Free Groups
For a finitely generated group Γ denote by μ(Γ) the growth coefficient of Γ, that is, the infimum over all real numbers d such that sn(Γ) < n!d. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. For a finitely generated group Γ denote by sn(Γ) the number of subgroups of inde...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2016
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498817501808