Abstract
We generalize Whitman's theorem on the representation of lattices by partition lattices or, which is the same, by subgroup lattices of a suitable group. A sufficient condition is stated for a group variety to be lattice-universal (i.e., every lattice has a presentation by the subgroup lattice of a group in this variety). As a consequence, we infer that every couniable lattice is representable by the subgroup lattice of a finitely generated free Burnside group of a large enough odd exponent.
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Additional information
Translated fromAlgebra i Logika, Vol. 35, No. 5, pp. 587–611, September–October, 1996.
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Repnitskii, V.B. Lattice universality of free burnside groups. Algebr Logic 35, 330–343 (1996). https://doi.org/10.1007/BF02367358
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DOI: https://doi.org/10.1007/BF02367358