On Nilpotent Multipliers of Pairs of Groups

TL;DR

This paper investigates the structure of nilpotent multipliers for pairs of finitely generated abelian groups, providing explicit descriptions and inequalities, advancing understanding in group theory.

Contribution

It determines the structure of nilpotent multipliers for pairs of finitely generated abelian groups with complements, and establishes inequalities for finite groups.

Findings

Explicit structure of nilpotent multipliers for certain abelian group pairs

Inequalities relating nilpotent multipliers of finite groups and their factors

Extension of known results to pairs with complements

Abstract

In this paper, we determine the structure of the nilpotent multipliers of all pairs $(G,N)$ of finitely generated abelian groups where $N$ admits a complement in $G$. Moreover, some inequalities for the nilpotent multipliers of pairs of finite groups and their factor groups are given.