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

Mohsen Parvizi; Behrooz Mashayekhy

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arXiv · 1202.2648

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

Mohsen Parvizi·Behrooz Mashayekhy

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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 $r_{i+1}\mid r_i \ \ (1\leq i\leq t-1)$, $c_1+c_2+1\geq n$, $2c_2-c_1>2n-2$ 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.

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BibTeX RIS

Mohsen Parvizi, Behrooz Mashayekhy. 2012-02-13. Some outer commutator multipliers and capability of nilpotent products of cyclic groups. https://arxiv.org/abs/1202.2648

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