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## Some Baer Invariants of Free Nilpotent Groups

### 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, $\textbf{Z}\st{n}* \textbf{Z}\st{n}*...\st{n}*\textbf{Z}$) 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 $(c_1,c_2,...,c_t)$, where $c_1\geq n$.Comment: 17 page

Topics: Mathematics - Group Theory, 20E34, 20E10, 20F18
Year: 2011
OAI identifier: oai:arXiv.org:1103.5151