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algebra universalis

, Volume 37, Issue 2, pp 253–255 | Cite as

A short proof of a theorem of Birkhoff

  • G. Grätzer
  • E.T. Schmidt
  • D. Wang

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.

Key words and phrases. Group, poset, autormorphism group, distributive lattice. 

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Copyright information

© Birkhäuser Verlag Basel, 1997

Authors and Affiliations

  • G. Grätzer
    • 1
  • E.T. Schmidt
    • 2
  • D. Wang
    • 3
  1. 1.Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba R 3T 2N2, Canada. E-mail: gratzer@ccu.umanitoba.caCA
  2. 2.Department of Mathematics, Transport Engineering Faculty, Technical University of Budapest, Müegyetem Rkp. 3, H-1521 Budapest, Hungary. E-mail: schmidt@euromath.vma.bme.huHU
  3. 3.Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba R 3T 2N2, Canada. E-mail: Dabin_Wang@umanitoba.caCA

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