Baumslag defined a family of groups that are of interest because they
closely resemble free groups, yet are not free. It was known that
each group in this family has the same lower central series of
quotients and the same first two terms in the derived series of
quotients as does the free group $F$ on two generators.
¶ We have verified that there are different isomorphism types among the
groups in the family, and that the third terms in the derived series
of quotients are often distinct from that of $F$. Our basic technique
is to count the number of homomorphisms from the groups of interest to
a target group.