Twisted Conjugacy Classes in R. Thompson’s Group F
In this article, we prove that any automorphism of R. Thompsons group F has infinitely many twisted conjugacy classes. The result follows from the work of Brin, together with standard facts about R. Thompsons group F, and elementary properties of the Reidemeister numbers.
Bleak, Collin; Fel'shtyn, Alexander; and Gonçalves, Daciberg L.. (2008). "Twisted Conjugacy Classes in R. Thompson’s Group F". Pacific Journal of Mathematics, 238(1), 1-6.