|The Conjugacy Problem in Extensions of Thompson's group F
Burillo, José; Matucci, Francesco; Ventura, Enric
We solve the twisted conjugacy problem on Thompson's group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut_+(F) are orbit decidable provided a certain conjecture on Thompson's group T is true. By using general criteria introduced by Bogopolski, Martino and Ventura in , we construct a family of free extensions of F where the conjugacy problem is unsolvable. As a byproduct of our techniques, we give a new proof of a result of Bleak-Fel'shtyn-Goncalves in  showing that F has property R_\infty, and which can be extended to show that Thompson's group T also has property R_\infty.