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Groups of binary relations

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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.

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References

  1. Birkhoff, G., Sóbre los grupos de automorfismos,Rev.Un.Math.Argentina, 11 (1946), 155–157.

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  2. Clifford, A. H. and G. B. Preston,The Algebraic Theory of Semigroups, Vol. I, Providence, 1961.

  3. Montague, J. S. and R. J. Plemmons, Maximal subgroups of the semigroup of relations,J.of Algebra, Vol. 13, 4 (1969), 575–587.

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  4. Plemmons, R. J. and M. T. West, On the semigroup of binary relations, to appear in thePacific J.Math.

  5. Schwarz, S., The semigroup of binary relations on a finite set, presented to theInternational Symposium on Semigroups, Bratislava, Czechoslovakia, June, 1968.

  6. Zareckii, K. A., The semigroup of binary relations (Russian),Mat.Sbornik 61 (1963), 291–305.

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Authors and Affiliations

  1. The University of Tennessee, 37916, Knoxville, Tennessee

    R. J. Plemmons & B. M. Schein

  2. The Saratov State University, Saratov, U.S.S.R.

    R. J. Plemmons & B. M. Schein

Authors
  1. R. J. Plemmons
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  2. B. M. Schein
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Plemmons, R.J., Schein, B.M. Groups of binary relations. Semigroup Forum 1, 267–271 (1970). https://doi.org/10.1007/BF02573046

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  • DOI: https://doi.org/10.1007/BF02573046

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