Algebra universalis

, 79:19 | Cite as

Submonoids of groups, and group-representability of restricted relation algebras

  • George M. Bergman
Part of the following topical collections:
  1. In memory of Bjarni Jónsson


Marek Kuczma asked in 1980 whether for every positive integer n, there exists a subsemigroup M of a group G, such that G is equal to the n-fold product \(M\,M^{-1} M\,M^{-1} \ldots \,M^{(-1)^{n-1}}\), but not to any proper initial subproduct of this product. We answer his question affirmatively, and prove a more general result on representing a certain sort of relation algebra by a family of subsets of a group. We also sketch several variants of the latter result.


Monoid Group Relation algebra Hilbert’s Hotel 

Mathematics Subject Classification

Primary 03G15 Secondary 06A06 20M20 


  1. 1.
    Gamow, G.: One, two, three...infinity. Viking Press, New York (1947)Google Scholar
  2. 2.
    Jónsson, B.: The theory of binary relations. In: Algebraic logic (Budapest, 1988). Colloq. Math. Soc. János Bolyai, vol. 54, pp. 245–292. North-Holland, Amsterdam (1991)Google Scholar
  3. 3.
    McKenzie, R.: Representations of integral relation algebras. Mich. Math. J. 17, 279–287 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Siebzehnte internationale Tagung über Funktionalgleichungen in Oberwolfach vom 17.6. bis 23.6.1979, Aequ. Math. 20, 286–315 (1980)Google Scholar
  5. 5.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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