Polynilpotent Multipliers of some Nilpotent Products of Cyclic Groups II

Details Polynilpotent Multipliers of some Nilpotent Products of Cyclic Groups II Polynilpotent Multipliers of some Nilpotent Products of Cyclic Groups II

2011-05-20

arxiv.org/abs/1105.4012v1

International Journal of Mathematics, Game Theory and Algebra, 17:5/6 (2008) 279-287

Mathematics

Group Theory

16 pages

Scientific paper

This article is devoted to present an explicit formula for the $c$th nilpotent multiplier of nilpotent products of some cyclic groups $G={\bf {Z}}\stackrel{n_1}{*}{\bf {Z}}\stackrel{n_2}{*}...\stackrel{n_{t-1}}{*}{\bf {Z}}\stackrel{n_{t}}{*} {\bf {Z}}_{m_{t+1}}\stackrel{n_{t+1}}{*}{\bf {Z}}_{m_{t+2}}\stackrel{n_{t+2}}{*}...\stackrel{n_{k}}{*}{\bf{Z}}_{m_{k+1}}$, where $m_{i+1} | m_i$ for all $t+1 \leq i \leq k$ and $c \geq n_1\geq n_2\geq ...\geq n_t\geq ...\geq n_{k}$ such that $ (p,m_{t+1})=1$ for all prime $p \leq n_1$. Moreover, we compute the polynilpotent multiplier of the group $G$ with respect to the polynilpotent variety ${\mathcal N}_{c_1,c_2,...,c_s}$, where $c_1 \geq n_1.$

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