224 citations · 695 across the 60 of their papers we have counts for
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Asymptotic dimension of relatively hyperbolic groups
D. V. Osin
Suppose that a finitely generated group is hyperbolic relative to a collection of subgroups . We prove that if each of the subgroups has fin…
Small cancellations over relatively hyperbolic groups and embedding theorems
D. V. Osin
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 finitel…
Relative Dehn functions of amalgamated products and HNN--extensions
D. V. Osin
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 c…
Elementary subgroups of relatively hyperbolic groups and bounded generation
D. V. Osin
Let be a group hyperbolic relative to a collection of subgroups . We say that a subgroup is hyperbolically embedded into , if is hyperbolic rel…
Algebraic entropy of elementary amenable groups
D. V. Osin
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 el…
Weak hyperbolicity and free constructions
D. V. Osin
The aim of this note is to show that weak relative hyperbolicity of a group relative to a subgroup (or relative hyperbolicity in the sense of Farb) does not imply any natural analo…