Some Baer Invariants of Free Nilpotent Groups

Details Some Baer Invariants of Free Nilpotent Groups Some Baer Invariants of Free Nilpotent Groups

2011-03-26

arxiv.org/abs/1103.5151v1

Journal of Algebra, 317 (2007) 365-375

Mathematics

Group Theory

17 pages

Scientific paper

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 $c_1\geq n$.

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