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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2000, Volume 231, Pages 323–331 (Mi tm521)  
This article is cited in 10 scientific papers (total in 10 papers)

Free Products of Finite Groups and Groups of Finitely Automatic Permutations

A. S. Oliinyk

National Taras Shevchenko University of Kyiv
Full-text PDF (212 kB) Citations (10)
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Abstract: A constructive proof is given to the isomorphic embeddability of a free product of a finite number of finite groups into a group of finitely automatic permutations over an alphabet in which the number of symbols is equal to the maximal order of the free factors.
Received in February 2000
Bibliographic databases:
UDC: 512.54
Language: Russian
Citation: A. S. Oliinyk, “Free Products of Finite Groups and Groups of Finitely Automatic Permutations”, Dynamical systems, automata, and infinite groups, Collected papers, Trudy Mat. Inst. Steklova, 231, Nauka, MAIK «Nauka/Inteperiodika», M., 2000, 323–331; Proc. Steklov Inst. Math., 231 (2000), 308–315
Citation in format AMSBIB
\Bibitem{Oli00}
\by A.~S.~Oliinyk
\paper Free Products of Finite Groups and Groups of Finitely Automatic Permutations
\inbook Dynamical systems, automata, and infinite groups
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2000
\vol 231
\pages 323--331
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm521}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1841761}
\zmath{https://zbmath.org/?q=an:1005.20023}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 231
\pages 308--315
Linking options:
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  • https://www.mathnet.ru/eng/tm/v231/p323
    • This publication is cited in the following 10 articles:
    1. Erschler A., Ozawa N., “Finite-Dimensional Representations Constructed From Random Walks”, Comment. Math. Helv., 93:3 (2018), 555–586  crossref  mathscinet  zmath  isi  scopus
    2. Gelander Ts., Golan G., Juschenko K., “Invariable generation of Thompson groups”, J. Algebra, 478 (2017), 261–270  crossref  mathscinet  zmath  isi  scopus
    3. Fedorova M., “Faithful Group Actions and Schreier Graphs”, Carpathian Math. Publ., 9:2 (2017), 202–207  crossref  mathscinet  zmath  isi
    4. Savchuk D., Vorobets Ya., “Automata generating free products of groups of order 2”, J Algebra, 336:1 (2011), 53–66  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Vorobets M., Vorobets Ya., “On a series of finite automata defining free transformation groups”, Groups Geometry and Dynamics, 4:2 (2010), 377–405  crossref  mathscinet  zmath  isi  scopus
    6. Erschler A., “Automatically presented groups”, Groups Geometry and Dynamics, 1:1 (2007), 47–59  crossref  mathscinet  zmath  isi
    7. Lavrenyuk Ya., Mazorchuk V., Oliynyk A., Sushchansky V., “Faithful group actions on rooted trees induced by actions of quotients”, Communications in Algebra, 35:11 (2007), 3759–3775  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Erschler A., “Piecewise automatic groups”, Duke Mathematical Journal, 134:3 (2006), 591–613  crossref  mathscinet  zmath  isi  elib  scopus
    9. Glasner Y., Mozes S., “Automata and square complexes”, Geometriae Dedicata, 111:1 (2005), 43–64  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Olijnyk A., Sushchansky V., “Representations of free products by infinite unitriangular matrices over finite fields”, International Journal of Algebra and Computation, 14:5–6 (2004), 741–749  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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