I am searching for a directly proof of the fact that: If $G$ is f.g. torsion-free nilpotent group, then every (nontrivial) $x \in G$, $x \notin G^{p}$ for all, but finitely many primes $p$
$x$ survives in $G/G^{p}$
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abstract-algebra
group-theory
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0I think that I found a reference("Lectures notes on nilpotent groups", Baumslag). Thank you very much for your time. – 2012-10-14