Rationally powered nilpotent group

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This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: rationally powered group and nilpotent group
View other group property conjunctions OR view all group properties


A group is termed a rationally powered nilpotent group if it satisfies the following equivalent conditions:

  1. It is both a rationally powered group and a nilpotent group.
  2. It is a nilpotent group and its abelianization is a rationally powered group.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness Reverse implication failure
Lazard Lie group Global Lazard Lie group|FULL LIST, MORE INFO
torsion-free nilpotent group |FULL LIST, MORE INFO
divisible nilpotent group |FULL LIST, MORE INFO