Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Osin, D. V."'
Autor:
Olshanskii, A. Yu., Osin, D. V.
We construct first examples of non-trivial groups without non-cyclic free subgroups whose reduced $C^\ast$-algebra is simple and has unique trace. This answers a question of de la Harpe. Both torsion and torsion free examples are provided. In particu
Externí odkaz:
http://arxiv.org/abs/1401.7300
Publikováno v:
Topology and its Applications, 2013, 160:16, 2104-2120
A group $G$ is called hereditarily non-topologizable if, for every $H\le G$, no quotient of $H$ admits a non-discrete Hausdorff topology. We construct first examples of infinite hereditarily non-topologizable groups. This allows us to prove that c-co
Externí odkaz:
http://arxiv.org/abs/1210.7895
We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity constants
Externí odkaz:
http://arxiv.org/abs/math/0701365
Autor:
Olshanskii, A. Yu., Osin, D. V.
We first give a short group theoretic proof of the following result of Lackenby. If $G$ is a large group, $H$ is a finite index subgroup of $G$ admitting an epimorphism onto a non--cyclic free group, and $g$ is an element of $H$, then the quotient of
Externí odkaz:
http://arxiv.org/abs/math/0601589
Autor:
Osin, D. V.
Suppose that a finitely generated group $G$ is hyperbolic relative to a collection of subgroups $\{H_1, ..., H_m\} $. We prove that if each of the subgroups $H_1, ..., H_m$ has finite asymptotic dimension, then asymptotic dimension of $G$ is also fin
Externí odkaz:
http://arxiv.org/abs/math/0411585
Autor:
Osin, D. V.
We generalize the small cancellation theory over hyperbolic groups developed by Olshanskii to the case of relatively hyperbolic groups. This allows us to construct infinite finitely generated groups with exactly $n$ conjugacy classes for every $n\ge
Externí odkaz:
http://arxiv.org/abs/math/0411039
Autor:
Osin, D. V.
We obtain an upper bound for relative Dehn functions of amalgamated products and HNN--extensions with respect to certain collections of subgroups. Our main results generalize the combination theorems for relatively hyperbolic groups proved by Dahmani
Externí odkaz:
http://arxiv.org/abs/math/0411027
Autor:
Osin, D. V.
Let $G$ be a group hyperbolic relative to a collection of subgroups $\{H_\lambda ,\lambda \in \Lambda \} $. We say that a subgroup $Q\le G$ is hyperbolically embedded into $G$, if $G$ is hyperbolic relative to $\{H_\lambda ,\lambda \in \Lambda \} \cu
Externí odkaz:
http://arxiv.org/abs/math/0404118
Autor:
Erschler, A. G., Osin, D. V.
We show that for any metric space $M$ satisfying certain natural conditions, there is a finitely generated group $G$, an ultrafilter $\omega $, and an isometric embedding $\iota $ of $M$ to the asymptotic cone ${\rm Cone}_\omega (G)$ such that the in
Externí odkaz:
http://arxiv.org/abs/math/0404111
Autor:
Osin, D. V.
We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of uniformly exponent
Externí odkaz:
http://arxiv.org/abs/math/0404075