Isomorphism Classes and Derived Series of Certain Almost-Free Groups

Abstract

Baumslagdefined 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 hasthe samelower central series of quotients and the same first two terms in the derived seriesof 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 seriesof quotients are often distinct from that of F. Our basic technique isto count the number of homomorphisms from the groups of interest to a target group.