Journal of Algebra, ( ISI ), Volume (320), Year (2008-6) , Pages (3269-3277)

#### Title : ( On nilpotent multipliers of some verbal products of groups )

Authors: , Behrooz Mashayekhy Fard ,

Citation: BibTeX | EndNote

#### Abstract

The paper is devoted to finding a homomorphic image for the $c$-nilpotent multiplier of the verbal product of a family of groups with respect to a variety ${\mathcal V}$ when ${\mathcal V} \subseteq {\mathcal N}_{c}$ or ${\mathcal N}_{c}\subseteq {\mathcal V}$. Also a structure of the $c$-nilpotent multiplier of a special case of the verbal product, the nilpotent product, of cyclic groups is given. In fact, we present an explicit formula for the $c$-nilpotent multiplier of the $n$th nilpotent product of the group $G= {\bf {Z}}\stackrel{n}{*}...\stackrel{n}{*}{\bf {Z}}\stackrel{n}{*} {\bf {Z}}_{r_1}\stackrel{n}{*}...\stackrel{n}{*}{\bf{Z}}_{r_t}$, where $r_{i+1}$ divides $r_i$ for all $i$, $1 \leq i \leq t-1$, and $(p,r_1)=1$ for any prime $p$ less than or equal to $n+c$, for all positive integers $n$, $c$.

#### Keywords

Nilpotent multiplier; Verbal product; Nilpotent product; Cyclic group.
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@article{paperid:1008866,
author = {, and Mashayekhy Fard, Behrooz},
title = {On nilpotent multipliers of some verbal products of groups},
journal = {Journal of Algebra},
year = {2008},
volume = {320},
month = {June},
issn = {0021-8693},
pages = {3269--3277},
numpages = {8},
keywords = {Nilpotent multiplier; Verbal product; Nilpotent product; Cyclic group.},
}