Nilpotent group that is powered for a set of primes

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This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: powered group for a set of primes and nilpotent group
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Definition

Suppose G is a group and \pi is a set of primes. We say that G is a \pi-powered nilpotent group if it satisfies the following equivalent conditions:

  1. G is a \pi-powered group and is also a nilpotent group.
  2. G is a nilpotent group that is both \pi-divisible and \pi-torsion-free.

Equivalence of definitions

Part of the proof relies on equivalence of definitions of nilpotent group that is torsion-free for a set of primes.