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2005 | 25 | 1 | 119-134
Tytuł artykułu

Representations of a free group of rank two by time-varying Mealy automata

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Abstrakty
EN
In the group theory various representations of free groups are used. A representation of a free group of rank two by the so-calledtime-varying Mealy automata over the changing alphabet is given. Two different constructions of such automata are presented.
Twórcy
autor
  • Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Bibliografia
  • [1] S.V. Aleshin, A free group of finite automata, (Russian), Vestnik Moskov. Univ. Ser. I. Mat. Mekh. 38 (1983), 12-14 (English Transl.: Moscow Univ. Math. Bull. 38 (1983), No. 4, 10-13).
  • [2] L. Bartholdi, R.I. Grigorchuk and V. Nekrashevych, From fractal groups to fractal sets, 'Fractals in Graz 2001', Birkhäuser, Basel 2003, 25-118.
  • [3] R.I. Grigorchuk, V. V. Nekrashevich and V.I. Sushchanskii, Automata, Dynamical Systems and Groups, Proc. Steklov Inst. Math. 231 (2000), 128-203.
  • [4] R.I. Grigorchuk and A. Żuk, Lectures on Automata Groups, Dynamics on Tress, and L2-invariants, 'Advanced Course on Automata Groups' (July 5-16, 2004 at CRM), Centre de Recerca Matemàtica, Universitat Autonòma de Barcelona, Bellaterra, Spain, (preprint, 2004).
  • [5] A. Olijnyk, Free products of C2 as groups of finitely automatic permutations, (in Russian), Voprosy Algebry 14 (1999), 158-165.
  • [6] A.S. Olijnyk and V.I. Sushchanskii, Free Groups of Infinitely Unitriangular Matrices, Math. Notes 67 (2000), 320-324.
  • [7] V.I. Sushchanskii, Group of Automatic Permutations, (Ukrainian), Dopov. Nats. Akad. Ukr. Mat. Prirodozn. Tekh. Nauki 1998, no. 6, 47-51.
  • [8] V.I. Sushchanskii, Group of Finite Automatic Permutations, (Ukrainian), Dopov. Nats. Akad. Ukr. Mat. Prirodozn. Tekh. Nauki 1999, no. 2, 48-52.
  • [9] A. Woryna, On transformations given by time-varying Mealy automata, (Polish), Zeszyty Nauk. Politech. Śląskiej, no. 1581, Ser. Automatyka 138 (2003), 201-215.
  • [10] A. Woryna, On the group permutations generated by time-varying Mealy automata, Publ. Math. Debrecen, 67 (2005), 115-130.
  • [11] A. Woryna, On representation of a semidirect product of cyclic groups by a 2-state time-varying Mealy automaton, Zeszyty Nauk. Politech. Śląskiej, no. 1652, Ser. Math. 91 (2004), 343-355.
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1095
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