# Finitely generated free nilpotent group

From Groupprops

## Contents

## Definition

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

## 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 |