Oleg Bogopolski

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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)
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)
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)
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)