Open main menu

Groupprops β

Finitely generated free nilpotent group

Contents

Definition

A group is termed a finitely generated free nilpotent group if there exist nonnegative integers d and c such that the group is the free nilpotent group of nilpotency class c on a generating set of size d.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finitely generated free abelian group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
free nilpotent group |FULL LIST, MORE INFO
torsion-free nilpotent group |FULL LIST, MORE INFO