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Diskr. Mat., 1999, Volume 11, Issue 4, Pages 101–109 (Mi dm392)  

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

On a consequence of the Krohn–Rhodes theorem

S. V. Aleshin


Abstract: The Krohn–Rhodes theorem on the cascade connected automata was proved under the assumption that the basis contains special group automata. In this paper, we show that if the basis contains the constant automata, then this restriction can be omitted and for any simple group $G$ it is sufficient to take an arbitrary group automaton, whose group has $G$ as a divisor.

DOI: https://doi.org/10.4213/dm392

Full text: PDF file (862 kB)

English version:
Discrete Mathematics and Applications, 1999, 9:6, 583–592

Bibliographic databases:

UDC: 519.7
Received: 15.02.1999

Citation: S. V. Aleshin, “On a consequence of the Krohn–Rhodes theorem”, Diskr. Mat., 11:4 (1999), 101–109; Discrete Math. Appl., 9:6 (1999), 583–592

Citation in format AMSBIB
\Bibitem{Ale99}
\by S.~V.~Aleshin
\paper On a consequence of the Krohn--Rhodes theorem
\jour Diskr. Mat.
\yr 1999
\vol 11
\issue 4
\pages 101--109
\mathnet{http://mi.mathnet.ru/dm392}
\crossref{https://doi.org/10.4213/dm392}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1761016}
\zmath{https://zbmath.org/?q=an:0966.68100}
\transl
\jour Discrete Math. Appl.
\yr 1999
\vol 9
\issue 6
\pages 583--592


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  • http://mi.mathnet.ru/eng/dm/v11/i4/p101

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Aleshin, “Automata in algebra”, J. Math. Sci., 168:1 (2010), 14–20  mathnet  crossref  mathscinet  elib
    2. Letunovskii A.A., “O zadache vyrazimosti avtomatov otnositelno superpozitsii dlya sistem s fiksirovannoi dobavkoi”, Intellektualnye sistemy v proizvodstve, 2012, no. 1, 36–50  elib
    3. A. A. Letunovskii, “Cycle indices of an automaton”, Discrete Math. Appl., 23:5-6 (2013), 445–450  mathnet  crossref  crossref  mathscinet  elib
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