Orbit decidability and the conjugacy problem for some extensions of groups

Details Orbit decidability and the conjugacy problem for some extensions of groups Orbit decidability and the conjugacy problem for some extensions of groups

2007-12-19

arxiv.org/abs/0712.3104v1

Mathematics

Group Theory

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Orbit decidability and the conjugacy problem for some extensions of groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orbit decidability and the conjugacy problem for some extensions of groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orbit decidability and the conjugacy problem for some extensions of groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-146180