N. V. Bayanova, A. V. Zenkov, “Infinite distributivity in the lattice of varieties of <nobr>$m$</nobr>-groups”, Algebra Logika, 2015, Volume 54, Number 1,Pages <nobr>3

This article is cited in 1 paper

Infinite distributivity in the lattice of varieties of $m$-groups

N. V. Bayanova^a, A. V. Zenkov^b

^a Altai State University, pr. Lenina 61, Barnaul, 656049, Russia
^b Altai State Agricultural University, pr. Krasnoarmeiskii 98, Barnaul, 656049, Russia

Abstract: We construct an example showing that in the lattice of varieties of $m$-groups, the equality $\mathcal V\left(\bigvee_i\mathcal U_i\right)=\bigvee_i(\mathcal{VU}_i)$ does not always hold for an infinite set of indices.

Keywords: infinite distributivity, lattice of varieties of $m$-groups.

UDC: 512.54

Received: 02.02.2014

DOI: 10.17377/alglog.2015.54.101