Some Inequalities for Nilpotent Multipliers of Finite Groups

TL;DR

This paper establishes new inequalities relating to the order, exponent, and generators of the c-nilpotent multiplier of finite groups, especially p-groups, improving upon previous bounds in the literature.

Contribution

It introduces generalized inequalities for the c-nilpotent multiplier of finite groups, extending and refining earlier results by Jones and Moghaddam.

Findings

Derived inequalities for the order, exponent, and generators of the c-nilpotent multiplier

Extended results specifically for finite p-groups

Improved upon existing inequalities in the literature

Abstract

In this paper we present some inequalities for the order, the exponent and the number of generators of the $c$-nilpotent multiplier (the Baer invariant with respect to the variety of nilpotent groups of class at most $c \geq 1$) of a finite group and specially of a finite $p$-group. Our results generalize some previous related results of M.R. Jones and M.R.R. Moghaddam. Also, we show that our results improve some of the previous inequalities.