Abstract
One of the principal impulses for this paper was the consideration of the question, first raised in 1973 by G. Baumslag [2], of whether every finitely generated Abelian by polycyclic group can be embedded in a finitely presented Abelian by polycyclic group. That this cannot be done follows at once from THEOREM A. Every finitely presented Abelian by polycyclic group has a metanilpotent normal subgroup of finite index.
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