Some Functorial Properties of Nilpotent Multipliers

TL;DR

This paper investigates the functorial properties of the $c$-nilpotent multiplier of groups, focusing on its behavior as a functor and its interaction with Ext and Tor functors, providing explicit formulas for finitely generated abelian groups.

Contribution

It introduces new results on the functorial nature of the $c$-nilpotent multiplier and explores its commutativity with Ext and Tor functors, including explicit formulas.

Findings

Explicit formula for the $c$-nilpotent multiplier of finitely generated abelian groups

Demonstrates the functor's commutativity with Ext and Tor functors

Provides insights into the functorial properties of nilpotent multipliers

Abstract

In this paper, we are going to look at the $c$-nilpotent multiplier of a group $G$, ${\cal N}_cM(G)$, as a functor from the category of all groups, ${\cal G}roup$, to the category of all abelian groups, ${\cal A}b$, and focusing on some functional properties of it. In fact, by using some results of the first author and others and finding an explicit formula for the $c$-nilpotent multiplier of a finitely generated abelian group, we try to concentrate on the commutativity of the above functor with the two famous functors Ext and Tor.