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A Note On Subloop Lattices

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Abstract

Pálfy and Pudlák (Algebra Universalis 11, 22–27, 1980) posed the question: is every finite lattice isomorphic to an interval sublattice of the lattice of subgroups of a finite group? in this paper we will look at examples of lattices that can be realized as subloop lattices but not as subgroup lattices. This is a first step in answering a new question: is every finite lattice isomorphic to an interval sublattice of the subloop lattice of a finite loop?

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Adelphi University, Garden City, NY, 11010, USA

    Tuval Foguel

  2. Department of Mathematics, University of Florida, 1400 Stadium Rd, Gainesville, FL, 32611, USA

    Josh Hiller

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  1. Tuval Foguel
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  2. Josh Hiller
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Correspondence to Tuval Foguel.

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Foguel, T., Hiller, J. A Note On Subloop Lattices. Results. Math. 69, 11–21 (2016). https://doi.org/10.1007/s00025-015-0481-z

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  • DOI: https://doi.org/10.1007/s00025-015-0481-z

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