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Matematicheskie Zametki, 1998, Volume 63, Issue 2, Pages 248–259
DOI: https://doi.org/10.4213/mzm1271 (Mi mzm1271) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On free semigroups of automaton transformations

A. S. Oliinyk

National Taras Shevchenko University of Kyiv
Full-text PDF (248 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm1271
Abstract: It is established that the subset of free k-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set (in the sense of the Baire category approach) in the set of all k-generated subsemigroups. A continuum series of pairs of automaton transformations each of which generates a free semigroup of rank two is indicated. A criterion is established for this semigroup to be a finite-automaton group.
Received: 26.03.1996
English version:
Mathematical Notes, 1998, Volume 63, Issue 2, Pages 215–224
DOI: https://doi.org/10.1007/BF02308761
Bibliographic databases:
UDC: 512.534.3
Language: Russian
Citation: A. S. Oliinyk, “On free semigroups of automaton transformations”, Mat. Zametki, 63:2 (1998), 248–259; Math. Notes, 63:2 (1998), 215–224
Citation in format AMSBIB
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\by A.~S.~Oliinyk
\paper On free semigroups of automaton transformations
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\yr 1998
\vol 63
\issue 2
\pages 248--259
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\zmath{https://zbmath.org/?q=an:0920.20057}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 2
\pages 215--224
\crossref{https://doi.org/10.1007/BF02308761}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000075520700031}
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  • https://doi.org/10.4213/mzm1271
  • https://www.mathnet.ru/eng/mzm/v63/i2/p248
    • This publication is cited in the following 5 articles:
    1. E. Kochubinska, A. Oliynyk, “Monogenic free inverse semigroups and partial automorphisms of regular rooted trees”, Mat. Stud., 61:1 (2024), 3  crossref
    2. Andriy Oliynyk, Veronika Prokhorchuk, “On a finite state representation of GL(n,Z)”, ADM, 36:1 (2023), 74  crossref
    3. V. V. Doroshenko, “Most Transformation Semigroups Are Free”, Math. Notes, 87:3 (2010), 436–439  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Doroshenko, V, “Free subsemigroups in topological semigroups”, Semigroup Forum, 79:3 (2009), 427  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Holubowski, W, “The ubiquity of free subsemigroups of infinite triangular Matrices”, Semigroup Forum, 66:2 (2003), 231  crossref  mathscinet  zmath  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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