Finitely generated nilpotent group

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

Definition

Symbol-free definition

A finitely generated nilpotent group is a group satisfying the following equivalent conditions:

1. It is finitely generated and nilpotent
2. It is nilpotent and its abelianization is finitely generated

Equivalence of definitions

For full proof, refer: Equivalence of definitions of finitely generated nilpotent group