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 $G=\mathbf{Z}\stackrel{n_1}{\ast }\mathbf{Z}\stackrel{n_2}{\ast }...\stackrel{n_{t-1}}{\ast }\mathbf{Z}\stackrel{n_t}{\ast }{\mathbf{Z}}_{m_{t+1}}\stackrel{n_{t+1}}{\ast }{\mathbf{Z}}_{m_{t+2}}\stackrel{n_{t+2}}{\ast }...\stackrel{n_k}{\ast }{\mathbf{Z}}_{m_{k+1}}$, where $m_{i+1}|m_i$ for all $t+1\le i\le k$ and $c\ge n_1\ge n_2\ge ...\ge n_t\ge ...\ge n_k$ such that $(p,m_{t+1})=1$ for all prime $p\le n_1$. 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 $c_1\ge n_1.$

16 pages

Cited by in corpus (1)

• On the Order of Polynilpotent Multipliers of Some Nilpotent Products of Cyclic $p$-Groups