Abstract
In this paper, we generalize portions of the theory of localization to the category of nilpotent R-powered groups, where R is a binomial UFD. In particular, we show that if is a set of primes in R and G is a finitely R-generated nilpotent R-powered group, there exists a unique nilpotent R-powered -local group that is, in some sense, the best approximation to G among all nilpotent R-powered -local groups. We also use various residual properties of nilpotent R-powered groups to prove that every -localization map is an -isomorphism when R is a PID containing and G is finitely R-generated.
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