Algebra universalis

, 80:16 | Cite as

Lattices with many congruences are planar

  • Gábor CzédliEmail author
Open Access


Let L be an n-element finite lattice. We prove that if L has more than \(2^{n-5}\) congruences, then L is planar. This result is sharp, since for each natural number \(n\ge 8\), there exists a non-planar lattice with exactly \(2^{n-5}\) congruences.


Planar lattice Lattice congruence Congruence lattice 

Mathematics Subject Classification




The referee’s historical comment calling the author’s attention to Crawley and Dilworth [2] and to Dilworth [4] is highly appreciated.


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Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary

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