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A short proof of a theorem of Birkhoff

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Abstract.

This paper gives a new proof of a theorem of G. Birkhoff: Every group \( {\goth G} \) can be represented as the automorphism group of a distributive lattice D; if \( {\goth G} \) is finite, D can be chosen to be finite. The new proof is short, and it is easily visualized.

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Authors and Affiliations

  1. Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba R 3T 2N2, Canada. E-mail: gratzer@ccu.umanitoba.ca, , , , , , CA

    G. Grätzer

  2. Department of Mathematics, Transport Engineering Faculty, Technical University of Budapest, Müegyetem Rkp. 3, H-1521 Budapest, Hungary. E-mail: schmidt@euromath.vma.bme.hu, , , , , , HU

    E.T. Schmidt

  3. Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba R 3T 2N2, Canada. E-mail: Dabin_Wang@umanitoba.ca, , , , , , CA

    D. Wang

Authors
  1. G. Grätzer
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  2. E.T. Schmidt
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  3. D. Wang
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Additional information

Received November 3, 1995; accepted in final form October 3, 1996.

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Grätzer, G., Schmidt, E. & Wang, D. A short proof of a theorem of Birkhoff. Algebra univers. 37, 253–255 (1997). https://doi.org/10.1007/s000120050017

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  • DOI: https://doi.org/10.1007/s000120050017

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