Bockstein theorem for nilpotent groups
Abstract
We extend the definition of Bockstein basis σ(G) to nilpotent groups G. A metrizable space X is called a Bockstein space if G(X) = \H(X) | H∈ σ(G)\ for all Abelian groups G. Bockstein First Theorem says that all compact spaces are Bockstein spaces. Here are the main results of the paper: Let X be a Bockstein space. If G is nilpotent, then G(X) ≤ 1 if and only if \H(X) | H∈σ(G)\≤ 1. X is a Bockstein space if and only if _(l) (X) = Z(l)(X) for all subsets l of prime numbers.
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