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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 5, Pages 1102–1119 (Mi smj2149)  
This article is cited in 1 scientific paper (total in 1 paper)

The groups of $ZC$-automaton transformations

A. S. Oliinyka, V. I. Sushchanskiĭb

a Taras Shevchenko Kiev National University, Kiev, Ukraine
b Institute of Mathematics, Silesian University of Technology, Gliwice, Poland
Full-text PDF (426 kB) Citations (1)
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Abstract: Under study are the $ZC$-automata and the transformation groups determined by them. We establish relationships between the group of $ZC$-automaton transformations and the group of infinite unitriangular integer matrices. We describe the derived series of the group of $ZC$-automaton transformations and present conditions for the representability of residually solvable groups by $ZC$-automaton transformations. We construct a continual family of $ZC$-automata with two states, each of which generates a free semigroup.
Keywords: automaton, automaton transformation, unitriangular matrix, residually solvable group, derived series, free semigroup.
Received: 10.09.2009
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 5, Pages 879–891
DOI: https://doi.org/10.1007/s11202-010-0088-2
Bibliographic databases:
Document Type: Article
UDC: 512.54
Language: Russian
Citation: A. S. Oliinyk, V. I. Sushchanskiǐ, “The groups of $ZC$-automaton transformations”, Sibirsk. Mat. Zh., 51:5 (2010), 1102–1119; Siberian Math. J., 51:5 (2010), 879–891
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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