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Algebra universalis

, 79:19 | Cite as

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

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

Abstract

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.

Keywords

Monoid Group Relation algebra Hilbert’s Hotel 

Mathematics Subject Classification

Primary 03G15 Secondary 06A06 20M20 

References

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    McKenzie, R.: Representations of integral relation algebras. Mich. Math. J. 17, 279–287 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
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    Siebzehnte internationale Tagung über Funktionalgleichungen in Oberwolfach vom 17.6. bis 23.6.1979, Aequ. Math. 20, 286–315 (1980)Google Scholar
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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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