Orbit decidability and the conjugacy problem for some extensions of groups
| dc.creator | Bogopolski, O. | |
| dc.creator | Martino, A. | |
| dc.creator | Ventura, E. | |
| dc.date | 2007-12-19 | |
| dc.date.accessioned | 2026-07-07T08:50:17Z | |
| dc.date.available | 2026-07-07T08:50:17Z | |
| dc.description | 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 $A\leqslant Aut(F)$ is orbit decidable. From this, we deduce that the conjugacy problem is solvable, among others, for all groups of the form $\mathbb{Z}^2\rtimes F_m$, $F_2\rtimes F_m$, $F_n \rtimes \mathbb{Z}$, and $\mathbb{Z}^n \rtimes_A F_m$ with virtually solvable action group $A\leqslant GL_n(\mathbb{Z})$. Also, we give an easy way of constructing groups of the form $\mathbb{Z}^4\rtimes F_n$ and $F_3\rtimes F_n$ with unsolvable conjugacy problem. On the way, we solve the twisted conjugacy problem for virtually surface and virtually polycyclic groups, and give an example of a group with solvable conjugacy problem but unsolvable twisted conjugacy problem. As an application, an alternative solution to the conjugacy problem in $Aut(F_2)$ is given. | |
| dc.identifier | https://arxiv.org/abs/0712.3104 | |
| dc.identifier | http://arxiv.org/abs/0712.3104 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144553 | |
| dc.subject | Group Theory | |
| dc.subject | 20F10; 20F28 | |
| dc.title | Orbit decidability and the conjugacy problem for some extensions of groups | |
| dc.type | text |