Some outer commutator multipliers and capability of nilpotent products of cyclic groups

Abstract

In this paper, first we obtain an explicit formula for an outer commutator multiplier of nilpotent products of cyclic groups with respect to the variety $[{\mathfrak{N}}_{c_1},{\mathfrak{N}}_{c_2}]$, $\mathfrak{N}_{c}M(\mathbb{Z}\st{n}* \mathbb{Z}\st{n}* ... \st{n}* \mathbb{Z}\st{n}* \mathbb{Z}_{r_1}\st{n}* \mathbb{Z}_{r_2}\st{n}* ... \st{n}* \mathbb{Z}_{r_t})$ where $r_{i+1}\mid r_i(1\le i\le t-1)$, $c_1+c_2+1\ge n$, $2c_2-c_1>2n-2$ and $(p,r_1)=1$ for all prime less than or equal $c_1+c_2+n$, second we give a necessary condition for these groups to be $[{\mathfrak{N}}_{c_1},{\mathfrak{N}}_{c_2}]$-capable.

13 pages

References in corpus (2)

• On the Nilpotent Multiplier of a Free Product
• Higher Schur-multiplicator of a Finite Abelian Group