Given a directed-complete partial order of finitely presented groups, I want to say that the free group is the bottom, but I don't think that is right.

Can anyone say what is a typical bottom in a directed-complete partial order of groups? Furthermore, are the finitely presentable groups the finite or compact elements?

actually made it incorrect.One should speak of a DCPO of groups, not of "DCPO groups". Moreover, why not insert the definite or indefinite article before the word "bottom" if you feel these changes areso necessary as to warrant bumping this question? – Yemon Choi Jun 4 at 14:02