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ABSTRACT
We prove that the fundamental group of a 3-manifold is contained in the class of groups that satisfies the strong Bass conjecture over
. Our interest in
arises from its strong closure properties. We also show that the class consisting of those groups whose elements do not satisfy Baumslag-Solitar relations of the form
for all
is quite large and has interesting closure properties as well. Each group in this class satisfies the strong Bass conjecture over k, where k is a subring of
with
.
ACKNOWLEDGMENT
I would like to thank I. Emmanouil for interesting discussions related to the topic of this paper.