Polynilpotent Multipliers of Some Nilpotent Products of Cyclic Groups

Abstract

In this article, we present an explicit formula for the $c$th nilpotent multiplier (the Baer invariant with respect to the variety of nilpotent groups of class at most $c\ge 1$) of the $n$th nilpotent product of some cyclic groups $G=\mathbb{Z}\stackrel{n}{\ast }...\stackrel{n}{\ast }\mathbb{Z}\stackrel{n}{\ast }{\mathbb{Z}}_{r_1}\stackrel{n}{\ast }...\stackrel{n}{\ast }{\mathbb{Z}}_{r_t}$, (m-copies of $\mathbb{Z}$), where $r_{i+1}|r_i$ for $1\le i\le t-1$ and $c\ge n$ such that $(p,r_1)=1$ for all primes $p$ less than or equal to $n$. Also, we compute the polynilpotent multiplier of the group $G$ with respect to the polynilpotent variety ${\mathcal{N}}_{c_1,c_2,...,c_t}$, where $c_1\ge n.$

13 pages, To appear in The Arabian Journal for Science and Engineering-Mathematics

References in corpus (1)

• Higher Schur-multiplicator of a Finite Abelian Group