Fitting quotients of finitely presented abelian-by-nilpotent groups

TL;DR

This paper demonstrates that any finitely generated nilpotent group of class 2 can be realized as a quotient of a finitely presented abelian-by-nilpotent group by its largest nilpotent normal subgroup, revealing a structural relationship.

Contribution

It establishes a universal construction linking finitely generated nilpotent groups of class 2 to finitely presented abelian-by-nilpotent groups, expanding understanding of their quotient structures.

Findings

Every finitely generated nilpotent group of class 2 appears as a specific quotient.

Finitely presented abelian-by-nilpotent groups can generate all such nilpotent groups as quotients.

The largest nilpotent normal subgroup plays a key role in this quotient relationship.

Abstract

We show that every finitely generated nilpotent group of class 2 occurs as the quotient of a finitely presented abelian-by-nilpotent group by its largest nilpotent normal subgroup.