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The Closures of Wreath Products in Product Action

Algebra and Logic Aims and scope

Let m be a positive integer and let Ω be a finite set. The m-closure of G ≤ Sym(Ω) is the largest permutation group G(m) on Ω having the same orbits as G in its induced action on the Cartesian product Ωm. An exact formula for the m-closure of the wreath product in product action is given. As a corollary, a sufficient condition is obtained for this m-closure to be included in the wreath product of the m-closures of the factors.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. V. Vasil’ev & I. N. Ponomarenko

  2. Novosibirsk State University, Novosibirsk, Russia

    A. V. Vasil’ev

  3. Steklov Institute of Mathematics, St. Petersburg Branch, St. Petersburg, Russia

    I. N. Ponomarenko

Authors
  1. A. V. Vasil’ev
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  2. I. N. Ponomarenko
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Correspondence to A. V. Vasil’ev.

Additional information

Supported by Mathematical Center in Akademgorodok, Agreement with RF Ministry of Education and Science No. 075-15-2019-1613.

Translated from Algebra i Logika, Vol. 60, No. 3, pp. 286-297, May-June, 2021. Russian DOI: https://doi.org/10.33048/alglog.2021.60.302.

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Vasil’ev, A.V., Ponomarenko, I.N. The Closures of Wreath Products in Product Action. Algebra Logic 60, 188–195 (2021). https://doi.org/10.1007/s10469-021-09640-0

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  • DOI: https://doi.org/10.1007/s10469-021-09640-0

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