The conjugacy problem in extensions of Thompson's group F

Abstract

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 [5], 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 [4] showing that F has property R_\infty, and which can be extended to show that Thompson's group T also has property R_\infty.

31 pages, 2 figures; improved exposition

References in corpus (1)

• The Geometric Invariants of Group Extensions

Cited by in corpus (2)

• Twisted conjugacy in Richard Thompson's group T
• Public key cryptography based on some extensions of group