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Sul problema di Burnside per i semigruppi e i linguaggi

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Si presentano alcuni recenti risultati (senza le dimostrazioni) sul problema di Burnside per i semigruppi (risp. gruppi) e si discutono brevemente alcuni problemi aperti. Si considera inoltre il cosiddetto problema di Burnside per i linguaggi. Si analizzano analogie e differenze con il precedente problema e si forniscono alcuni recenti teoremi.

Summary

Some recent results on the Burnside problem for semigroups (resp. groups) are given, without proofs, and some open problems are briefly discussed. Moreover the so-called Burnside problem for languages is considered. Analogies and differences with the preceding problem are analyzed and some recent theorems are given.

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Bibliografia

  1. Morse M. eHedlund G.,Unending chess, symbolic dynamics and a problem in semigroups. Duke Math. J., 11 (1944) 1–7.

    Article  MATH  MathSciNet  Google Scholar 

  2. Thue A.,Uber unendliche Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 7 (1906) 1–22. —,Uber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 1 (1912) 1–67.

    Google Scholar 

  3. Lothaire M., «Combinatorics on Words» Encyclopedia of Mathematics and its Applications, vol. 17, Addison-Wesley Publ. Company, 1983.

  4. Golod E. S.,On nil-algebras and residually finite p-groups. Izv. Nauk. Ser. Mat. 28 (1964) 273–276.

    MathSciNet  Google Scholar 

  5. Golod E. S. eShafarevich I.,On class field towers. Izv. Nauk. Ser. Mat. 28 (1964) 261–272.

    MATH  Google Scholar 

  6. Hall M., «The theory of Group». The McMillan Company, 1973.

  7. Green J. A. eRees D.,On semigroups in which xr=x. Math. Proc. Cambridge Phil. Soc., 48 (1952) 35–40.

    Article  MATH  MathSciNet  Google Scholar 

  8. Novikov P. S. eAdjan S. I.,Infinite periodic groups. Izv. Akad. Nauk. SSR Ser. Mat. 32 1, 2, 3 (1968) 212–244, 251–524, 709–731.

    MathSciNet  Google Scholar 

  9. Adjan S. I., «The Burnside problem and identities in groups». Springer Berlin (1978).

    Google Scholar 

  10. Hotzel E.,On finiteness conditions in semigroups. J. of Algebra 60 (1979) 352–370.

    Article  MATH  MathSciNet  Google Scholar 

  11. Coudrain M. eSchützenberger M. P.,Une condition de finitude des monoïdes finiment engendrés. C. R. Acad. Sc. Paris, Série A, 262 (1966) 1149–1151.

    MATH  Google Scholar 

  12. Simon I.,Conditions de finitude pour des semigroupes. C. R. Acad. Sc. Paris, Série A, 290 (1980) 1081–1082.

    MATH  Google Scholar 

  13. de Luca A. eRestivo A.,A finiteness conditions for finitely generated semigroups. Semigroup Forum 28 (1984) 123–134.

    Article  MATH  MathSciNet  Google Scholar 

  14. Restivo A. eReutenauer C.,On the Burnside problem for semigroups. J. of Algebra 89 (1984) 102–104.

    Article  MATH  MathSciNet  Google Scholar 

  15. Shirshov A. I.,On certain non associative nil rings and algebrais algebras. Mat. Sb. 41 (1957) 381–394.

    MathSciNet  Google Scholar 

  16. Curzio M., Longobardi P. eMay M.,Su di un problema combinatorio in teoria dei gruppi. Rendiconti dell’Accademia Nazionale dei Lincei 54 (1983) 136–142.

    Google Scholar 

  17. de Luca A. (1983), Manoscritto.

  18. Eilenberg S., «Automata, Languages and Machines». Vol. A, 1974, Academic Press.

  19. Ehrenfeucht A., Parikh R. eRozenberg G.,Pumping Lemmas for regular Languages. SIAM J. of Comput. 10 (1981) 536–541.

    Article  MATH  MathSciNet  Google Scholar 

  20. Restivo A. eReutenauer C.,Some applications of a theorem of Shirshov to language theory. Information and Control 57 (1983) 205–213.

    Article  MATH  MathSciNet  Google Scholar 

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(Conferenza tenuta il 16 maggio 1983)

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De Luca, A. Sul problema di Burnside per i semigruppi e i linguaggi. Seminario Mat. e. Fis. di Milano 53, 207–220 (1983). https://doi.org/10.1007/BF02924898

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