Semigroup Forum

, Volume 1, Issue 1, pp 267–271 | Cite as

Groups of binary relations

  • R. J. Plemmons
  • B. M. Schein
Short Notes

Abstract

It was shown in [3] that every finite group is the maximal subgroup of a semigroupB x of all binary relations on some finite set X. This result is extended here to arbitrary groups.

Keywords

Partial Order Finite Group Binary Relation Distributive Lattice Symmetric Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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  3. 3.
    Montague, J. S. and R. J. Plemmons, Maximal subgroups of the semigroup of relations,J.of Algebra, Vol. 13, 4 (1969), 575–587.MATHCrossRefMathSciNetGoogle Scholar
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    Plemmons, R. J. and M. T. West, On the semigroup of binary relations, to appear in thePacific J.Math.Google Scholar
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    Schwarz, S., The semigroup of binary relations on a finite set, presented to theInternational Symposium on Semigroups, Bratislava, Czechoslovakia, June, 1968.Google Scholar
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    Zareckii, K. A., The semigroup of binary relations (Russian),Mat.Sbornik 61 (1963), 291–305.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1970

Authors and Affiliations

  • R. J. Plemmons
    • 1
    • 2
  • B. M. Schein
    • 1
    • 2
  1. 1.The University of TennesseeKnoxville
  2. 2.The Saratov State UniversitySaratovU.S.S.R.

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