Embedding of groups in groups with single-valued extraction of roots (Q1103723)

Using localization arguments in the group ring of a torsion free nilpotent group the author proves the following Theorem 1. Any locally polycyclic group with unique extraction of roots in \({\mathfrak AN}_ c\) can be embedded in a locally polycyclic divisible group with unique extraction of roots in the same variety. Here \({\mathfrak AN}_ c\) consists of groups with abelian c-th term of their lower central series. Theorem 2 states the same result with locally polycyclic replaced by locally of finite rational rank. Here the rational rank of an extension of two groups is equal to the sum of the rational ranks of the two components, while for abelian groups it is equal to the dimension of the tensor product by the rational numbers over the field of rationals.