arXiv subjects

Valerij Bardakov

Publications and source records attributed to Valerij Bardakov.

2 recordsLinked to original sources

arXiv2004

Twisted conjugacy in free groups and Makanin's question

We discuss the following question of G. Makanin from ``Kourovka notebook'': does there exist an algorithm to determine is for an arbitrary pair of words $U$ and $V$ of a free group $F_n$ and an arbitrary automorphism $ϕ\in Aut(F_n)$ the equation $ϕ(X) U = V X$ solvable in $F_n$? We give the affirmative answer in the case when an automorphism is virtually inner, i.e. some its non-zero power is an inner automorphism of $F_n$.

math.GR↗

arXiv2004

On the conjugacy problem for cyclic extensions of free groups

We study the conjugacy problem in cyclic extensions of free groups. It is shown that the conjugacy problem is solvable in split extensions of finitely generated free groups by virtually inner automorphisms. An algorithm for construction of the unique representative (the conjugacy normal form) for each conjugacy class is given.

math.GR↗