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:
- It is finitely generated and nilpotent
- It is nilpotent and its Abelianization is finitely generated
Equivalence of definitions
For full proof, refer: Equivalence of definitions of finitely generated nilpotent group