Polynilpotent Multipliers of some Nilpotent Products of Cyclic Groups II

Abstract: 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 $c_1 \geq n_1.$