Rationally powered nilpotent group

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

Definition

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				|FULL LIST, MORE INFO
torsion-free nilpotent group				|FULL LIST, MORE INFO
divisible nilpotent group				|FULL LIST, MORE INFO