Journal of Algebra, ( ISI ), Year (2007-3)

#### Title : Some Baer invariants of free nilpotent groups ( Some Baer invariants of free nilpotent groups )

Authors: Behrooz Mashayekhy Fard , Mohsen Parvizi ,

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#### Abstract

We present an explicit structure for the Baer invariant of a free $n$th nilpotent group (the $n$th nilpotent product of infinite cyclic groups, $\\textbf{ Z}\\st{n}* \\textbf{ Z}\\st{n}*\\ldots \\st{n}*\\textbf{ Z}$) with respect to the variety ${\\cal V}$ with the set of words $V=\\{[\\ga_{c_1+1},\\ga_{c_2+1}]\\}$, for all $c_1\\geq c_2$ and $2c_2-c_1>2n-2$. Also, an explicit formula for the polynilpotent multiplier of a free $n$th nilpotent group is given for any class row $(c_1,c_2,\\ldots,c_t)$, where $c_1\\geq n$.

We present an explicit structure for the Baer invariant of a free $n$th nilpotent group (the $n$th nilpotent product of infinite cyclic groups, $\\textbf{ Z}\\st{n}* \\textbf{ Z}\\st{n}*\\ldots \\st{n}*\\textbf{ Z}$) with respect to the variety ${\\cal V}$ with the set of words $V=\\{[\\ga_{c_1+1},\\ga_{c_2+1}]\\}$, for all $c_1\\geq c_2$ and $2c_2-c_1>2n-2$. Also, an explicit formula for the polynilpotent multiplier of a free $n$th nilpotent group is given for any class row $(c_1,c_2,\\ldots,c_t)$, where $c_1\\geq n$.

#### Keywords

Baer invariant; Free nilpotent group; Nilpotent product; Polynilpotent variety.
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@article{paperid:203837,
author = {Mashayekhy Fard, Behrooz and Parvizi, Mohsen},
title = {Some Baer invariants of free nilpotent groups},
journal = {Journal of Algebra},
year = {2007},
month = {March},
issn = {0021-8693},
keywords = {Baer invariant; Free nilpotent group; Nilpotent product; Polynilpotent variety.},
}