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Maximal Subsemigroups of Finite Transformation Semigroups K(n, r)

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Abstract

Let T n be the full transformation semigroup on the n-element set X n . For an arbitrary integer r such that 2 ≤ r ≤ n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = {α ∈¸ T n : |im α| ≤ r}. We also formulate the cardinal number of such subsemigroups which is an answer to Problem 46 of Tetrad in 1969, concerning the number of subsemigroups of T n .

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Teachers College, Hangzhou, 310036, P. R. China

    Hao Bo Yang & Xiu Liang Yang

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  1. Hao Bo Yang
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  2. Xiu Liang Yang
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This work is supported by N. S. F. of Zhejiang Province and Hangzhou Teachers College

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Yang, H.B., Yang, X.L. Maximal Subsemigroups of Finite Transformation Semigroups K(n, r). Acta Math Sinica 20, 475–482 (2004). https://doi.org/10.1007/s10114-004-0367-6

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  • DOI: https://doi.org/10.1007/s10114-004-0367-6

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