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An independence theorem for ordered sets of principal congruences and automorphism groups of bounded lattices

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Abstract

For a bounded lattice L, the principal congruences of L form a bounded ordered set Princ(L). G. Grätzer proved in 2013 that every bounded ordered set can be represented in this way. Also, G. Birkhoff proved in 1946 that every group is isomorphic to the group of automorphisms of an appropriate lattice. Here, for an arbitrary bounded ordered set P with at least two elements and an arbitrary group G, we construct a selfdual lattice L of length sixteen such that Princ(L) is isomorphic to P and the automorphism group of L is isomorphic to G.

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Authors and Affiliations

  1. Bolyai Institute, Szeged, University of Szeged, Aradi vértanúk tere 1, Hungary, 6720

    Gábor Czédli

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  1. Gábor Czédli
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Correspondence to Gábor Czédli.

Additional information

Communicated by L. Zádori

Dedicated to the memory of professor László Megyesi (1939–2015), former head of the Department of Algebra and Number Theory of the University of Szeged

This research was supported by NFSR of Hungary (OTKA), grant number K 115518.

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Czédli, G. An independence theorem for ordered sets of principal congruences and automorphism groups of bounded lattices. ActaSci.Math. 82, 3–18 (2016). https://doi.org/10.14232/actasm-015-817-8

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  • DOI: https://doi.org/10.14232/actasm-015-817-8

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