Polynilpotent Multipliers of Some Nilpotent Products of Cyclic Groups

Details Polynilpotent Multipliers of Some Nilpotent Products of Cyclic Groups Polynilpotent Multipliers of Some Nilpotent Products of Cyclic Groups

2011-03-26

arxiv.org/abs/1103.5148v1

Arabian Journal for science and Engineering-Mathematics 36:3 (2011) 415-421

Mathematics

Group Theory

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

Scientific paper

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 $c\geq 1$) of the $n$th nilpotent product of some cyclic groups $G={\mathbb {Z}}\stackrel{n}{*} ... \stackrel{n}{*}{\mathbb {Z}}\stackrel{n}{*} {\mathbb {Z}}_{r_1}\stackrel{n}{*} ... \stackrel{n}{*}{\mathbb{Z}}_{r_t}$, (m-copies of $\mathbb {Z}$), where $r_{i+1} | r_i$ for $1 \leq i \leq t-1$ and $c \geq n$ 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 $c_1 \geq n.$

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