Geodesic
Infinite distributivity in the lattice of varieties of $m$-groups
Algebra i logika, Tome 54 (2015) no. 1, pp. 3-15

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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. 
@article{AL_2015_54_1_a0,
     author = {N. V. Bayanova and A. V. Zenkov},
     title = {Infinite distributivity in the lattice of varieties of $m$-groups},
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     pages = {3--15},
     publisher = {mathdoc},
     volume = {54},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2015_54_1_a0/}
}
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N. V. Bayanova; A. V. Zenkov. Infinite distributivity in the lattice of varieties of $m$-groups. Algebra i logika, Tome 54 (2015) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/AL_2015_54_1_a0/