Are there finitely presented infinite groups with a finite class number?



Infinite groups with a finite class number
Denis Osin proved that there was a finitely generated infinite group with exactly two (count'em) conjugacy classes, but I can't seem to find any statement as to the finiteness of the presentation. (see [this paper by Ashot Minasian](http://eprints.soton.ac.uk/54841/) for references and more results).


