The first derived functor of the inverse limit and localization (Q1612157)

For a tower \(G\) of finitely generated nilpotent groups we denote by \(G_{(p)} \) its localization at a prime \(p\). It is shown that if \(\varprojlim^1G\) is nontrivial, then the canonical map \(\varprojlim^1G\to\prod_{\text{all primes}}\varprojlim^1G_{(p)}\) is an infinite-to-one covering. Another result concerning the first derived functor of the inverse limit and localization is also shown in this paper.