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Schützenberger groups ofH-classes in the semigroup of all binary relations on a set

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Abstract

In a recent paper [1972], R. L. Brandon, D. W. Hardy, and G. Markowsky, showed that the Schützenberger group Γ(H) of anH-class H inB X is isomorphic to the automorphism group of a lattice V associated with H. For H a group this result is due to K.A. Zaretskiî [1963]. In this note we show that a small modification of Zaretskiî's method for H a group simultaneously gives the result of Brandon, Hardy and Markowsky.

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References

  • 1963 K.A. Zaretskiî.Полугруппа бинарных отношений. (The semigroup of binary relations). Mat. Sb. 61 (1963), 291–305.

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  • 1972 R. L. Brandon, D. W. Hardy, and G. Markowsky.The Schützenberger group of an ℋ-class in the semigroup of binary relations. Semigroup Forum 5 (1972), 45–53.

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Authors and Affiliations

  1. Monash University, 3168, Clayton, Victoria, Australia

    G. B. Preston

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  1. G. B. Preston
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Communicated by A.H. Clifford

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Preston, G.B. Schützenberger groups ofH-classes in the semigroup of all binary relations on a set. Semigroup Forum 6, 260–262 (1973). https://doi.org/10.1007/BF02389130

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  • DOI: https://doi.org/10.1007/BF02389130

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