Abstract
In the paper, the problem of representing a finite inverse semigroup by partial transformations of a graph is treated. The notions of weighted graph and its weighted partial isomorphisms are introduced. The main result is that any finite inverse semigroup is isomorphic to the semigroup of weighted partial isomorphisms of a weighted graph. This assertion is a natural generalization of the Frucht theorem for groups.
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References
D. König,Theorie der endlichen und unendlichen Graphen, Leipzig (1936).
R. Frucht, “Herstellung von Graphen mit vorgegebener abstrakten Gruppe,”Compositio Math.,6, 239–250 (1938).
V. A. Molchanov, “Semigroups of mapping on graphs,”Semigroup Forum,27, 155–199 (1983).
V. A. Molchanov, “Concrete characterization of partial endomorphism semigroups of graphs,”Acta Sci. Math.,51, 349–363 (1987).
A. H. Clifford and G. B. Preston,The Algebraic Theory of Semigroups, Vol. 1, Amer. Math. Soc. (1961).
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Translated fromMatematicheskie Zametki, Vol. 61, No. 2, pp. 246–251, February, 1997.
This research was partially supported by the International Science Foundation under grant No. GSU 041049.
Translated by A. I. Shtern
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Nemirovskaya, N.A. Frucht theorem for inverse semigroups. Math Notes 61, 201–205 (1997). https://doi.org/10.1007/BF02355729
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DOI: https://doi.org/10.1007/BF02355729