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Mat. Zametki, 1998, Volume 63, Issue 2, Pages 248–259 (Mi mz1271)  

This article is cited in 3 scientific papers (total in 3 papers)

On free semigroups of automaton transformations

A. S. Oliinyk

National Taras Shevchenko University of Kyiv

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.

DOI: https://doi.org/10.4213/mzm1271

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English version:
Mathematical Notes, 1998, 63:2, 215–224

Bibliographic databases:

UDC: 512.534.3
Received: 26.03.1996

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
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 2
\pages 248--259
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\crossref{https://doi.org/10.4213/mzm1271}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629906}
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\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 2
\pages 215--224
\crossref{https://doi.org/10.1007/BF02308761}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Holubowski, W, “The ubiquity of free subsemigroups of infinite triangular Matrices”, Semigroup Forum, 66:2 (2003), 231  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Doroshenko, V, “Free subsemigroups in topological semigroups”, Semigroup Forum, 79:3 (2009), 427  crossref  mathscinet  zmath  isi  scopus  scopus
    3. V. V. Doroshenko, “Most Transformation Semigroups Are Free”, Math. Notes, 87:3 (2010), 436–439  mathnet  crossref  crossref  mathscinet  zmath  isi
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