  We continue with the functional approach to the P-versus-NP problem, begun in
[2, 3]. We previously constructed a monoid RM^P that is non-regular iff NP is
not P. We now construct homomorphic images of RM^P with interesting properties.
In particular, the homomorphic image M^P_poly of RM^P is finitely generated and
J^0-simple, and is non-regular iff NP is not P. The group of units of M^P_poly
is the famous Richard Thompson group V.
