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The Commutativity Relation in the Symmetric Semigroup

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Abstract

We compute the cardinality of the centralizer of an injection or surjection provided that the basic set is countable. We prove a formula for the cardinality of the set of conjugacy classes in the infinite symmetric group.

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References

  1. Skornyakov L. A., “Group unars,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 5, 65-69 (1977).

  2. Bochkin A. M., “Unars with separative monoids of endomorphisms,” Izv. Vuzov. Mat., No. 5, 71-74 (1983).

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Authors and Affiliations

  1. Institute of Mathematics, Voronezh State University, Russia

    V. A. Kolmykov

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  1. V. A. Kolmykov
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Kolmykov, V.A. The Commutativity Relation in the Symmetric Semigroup. Siberian Mathematical Journal 45, 931–934 (2004). https://doi.org/10.1023/B:SIMJ.0000042480.17442.5b

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  • DOI: https://doi.org/10.1023/B:SIMJ.0000042480.17442.5b

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