On endomorphisms of torsion-free hyperbolic groups (2009)
Let $H$ be a torsion-free $\delta$-hyperbolic group with respect to a finite generating set $S$. Let $a_1,..., a_n$ and $a_{1*},..., a_{n*}$ be elements of $H$ such that $a_{i*}$ is conjugate to...
On uniform conjugators in torsion-free hyperbolic groups (2009)
Bogopolski, O., Ventura, Enric
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ORBIT DECIDABILITY AND THE CONJUGACY PROBLEM FOR SOME EXTENSIONS OF GROUPS (2009)
O. Bogopolski, A. Martino, E. Ventura
Abstract. Given a short exact sequence of groups with certain conditions, 1 → F → G → H → 1, we prove that G has solvable conjugacy problem if and only if the corresponding action subgroup A...
A recursive presentation for Mihailova's subgroup (2009)
Bogopolski, O., Ventura, Enric
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A recursive presentation for Mihailova's subgroup (2008)
We give an explicit recursive presentation for Mihailova's subgroup $M(H)$ of $F_n \times F_n$ corresponding to a finite, concise and Peiffer aspherical presentation $H=< x_1,..., x_n \mid R_1,...,...
Orbit decidability and the conjugacy problem for some extensions of groups (2007)
Bogopolski, O., Martino, A., Ventura, E.
Given a short exact sequence of groups with certain conditions, $1\to F\to G\to H\to 1$, we prove that $G$ has solvable conjugacy problem if and only if the corresponding action subgroup $A\leqslant...
Orbit decidability and the conjugacy problem for some extensions of groups (2007)
Bogopolski, O., Martino, Armando, Ventura, Enric
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Subgroups of small index in Aut(Fn) and Kazhdan's property (T) (2007)
Bogopolski, O., Vikentiev, Ruslan
We give a series of interesting subgroups of finite index in Aut(Fn). One of them has index 42 in Aut(F3) and infinite abelianization. This implies that Aut(F3) does not have Kazhdan’s property (T)...
Bogopolski, O., Buskin, Nikolai, Buturlakin, Alexander
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and Universität Dortmund Fakultät für Mathematik (2007)
O. Bogopolski, Lehrstuhl Vi (algebra, A. Martino, E. Ventura
decidability and the conjugacy problem
The mean Dehn function of abelian groups (2006)
While Dehn functions, D(n), of finitely presented groups are very well studied in the literature, mean Dehn functions are much less considered. M. Gromov introduced the notion of mean Dehn function...
The mean dehn functions of Abelian groups (2006)
Bogopolski, O., Ventura, Enric
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The automorphism group of a free-by-cyclic groups in rank 2 (2006)
Bogopolski, O., Martino, A., Ventura, E.
Let $\phi$ be an automorphism of a free group $F_n$ of rank $n$, and let $M_{\phi}=F_n \rtimes_{\phi} \mathbb{Z}$ be the corresponding mapping torus of $\phi$. We study the group $Out(M_{\phi})$...
The automorphism group of a free-by-cyclic group in rank 2 (2005)
Bogopolski, O., Martino, Armando, Ventura, Enric
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Free-by-cyclic groups have solvable conjugacy problem (2004)
Bogopolski, O., Martino, A., Maslakova, O., Ventura, E.
We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed...