$c$-nilpotent multiplier of finite $p$-groups

TL;DR

This paper investigates the structure and bounds of the $c$-nilpotent multiplier in finite $p$-groups, providing explicit classifications and improving previous results in this area.

Contribution

It establishes exact sequences, bounds, and explicit structures for the $c$-nilpotent multiplier, and characterizes $c$-capable groups within specific classes.

Findings

Derived exact sequences for the $c$-nilpotent multiplier

Established upper bounds for finite $p$-groups

Classified $c$-capable groups among extra-special $p$-groups

Abstract

The aim of this work is to find some exact sequences on the $c$- nilpotent multiplier of a group $G$. We also give an upper bound for the $c$- nilpotent multiplier of finite $p$-groups and give the explicit structure of groups whose take the upper bound. Finally, we will get the exact structure of the $c$- nilpotent multiplier and determine $c$-capable groups in the class of extra-special and generalized extra-special $p$-groups. It lets us to have a vast improvement over the last results on this topic.