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- O. BOGOPOLSKI
- 2008

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 subgroups of free group automorphisms, and one of P. Brinkmann that one can determine whether two cyclic words in a free group are mapped to each other by some power… (More)

- O. BOGOPOLSKI
- 2007

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 Aut(F) is orbit decidable. From this, we deduce that the con-jugacy problem is solvable, among others, for all groups of the form Z 2 Fm, F 2 Fm, Fn Z, and Z n A Fm with… (More)

- Oleg Bogopolski, E. Ventura
- IJAC
- 2011

Let H be a torsion-free δ-hyperbolic group with respect to a finite generating set S.) for every word W in n variables and length up to a computable constant depending only on δ, ♯S and n r=1 |g r |. As a corollary we deduce, that there exists a computable constant C = C(δ, ♯S) such that for any endomorphism ϕ of H if ϕ(h) is conjugate to h for every… (More)

- O Bogopolski, A Martino, E Ventura
- 2008

Let φ be an automorphism of a free group F n of rank n, and let M φ = F n ⋊ φ Z be the corresponding mapping torus of φ. We study the group Out(M φ) under certain technical conditions on φ. Moreover, in the case of rank 2, we classify the cases when this group is finite or virtually cyclic, depending on the conjugacy class of the image of φ in GL 2 (Z).

- L Bartholdi, O Bogopolski
- 2009

We prove that the abstract commensurator of a nonabelian free group, an infinite surface group, or more generally of a group that splits appropriately over a cyclic subgroup, is not finitely generated. This applies in particular to all torsion-free word-hyperbolic groups with infinite outer automorphism group and abelianization of rank at least 2. We also… (More)

- O. Bogopolski, E. Ventura
- 2008

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 of a group, D mean (n), suggesting that in many cases it should grow much more slowly than the Dehn function itself. Using only elementary counting methods,… (More)

- O. BOGOPOLSKI
- 2008

We give an explicit recursive presentation for Mihailova's subgroup M (H) of F n × F n corre-construct a finitely generated recursively presented orbit undecidable subgroup of Aut(F 3).

- OLEG BOGOPOLSKI, KONSTANTIN SVIRIDOV, Konstantin Sviridov
- 2009

We will say that a group G possesses the Magnus property if for any two elements u, v ∈ G with the same normal closure, u is conjugate to v or v −1. We prove that some one-relator groups, including the fundamental groups of closed nonorientable surfaces of genus g > 3 possess this property. The analogous result for orientable surfaces of any finite genus… (More)

- O. Bogopolski
- 2010

commensurators of solvable Baumslag-Solitar groups Abstract commensurators of solvable Baumslag-Solitar groups Abstract commensurators of solvable Baumslag – Solitar groups Abstract We prove that for any n 2, the abstract commensurator group of the Baumslag – Solitar group BS(1, n) is isomorphic to the subgroup { 1 q 0 p | q ∈ Q, p ∈ Q * } of GL 2 (Q).

- Oleg Bogopolski, Olga Maslakova
- IJAC
- 2016