Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bockstein theorem for nilpotent groups   We extend the definition of Bockstein basis $\sigma(G)$ to nilpotent groups
$G$. A metrizable space $X$ is called a {\it Bockstein space} if $\dim_G(X) =
\sup\{\dim_H(X) | H\in \sigma(G)\}$ 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 $\dim_G(X) \leq 1$ if and only if $\sup\{\dim_H(X) |
H\in\sigma(G)\}\leq 1$.
  $X$ is a Bockstein space if and only if $\dim_{\Z_{(l)}} (X) =
\dim_{\hat{Z}_{(l)}}(X)$ for all subsets $l$ of prime numbers.

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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: solv-int