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Finite automata and Burnside's problem for periodic groups

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Abstract

New examples of infinite periodic finitely-generated groups are constructed. The elements of the groups are mappings of a set of words in an alphabet X into itself induced by finite Mealy automata. Estimates are given of the number of states and diagrams of the automata realizing the generating elements of the groups. There are three items in the literature cited.

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Literature cited

  1. A. G. Kurosh, Group Theory tin Russian], Moscow (1967).

  2. J. Horejš, “Transformations defining finite automata,” Problemy Kibernetiki, No. 9, 23–26 (1963).

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  3. E. S. Golod, “Nil-algebras and finitely-approximatable groups,” Izv. Akad. Nauk SSSR, Ser. Matem.,28, No. 2, 273–276 (1964).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    S. V. Aleshin

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  1. S. V. Aleshin
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Additional information

Translated from Matematicheskie Zametki, Vol. 11, No. 3, pp. 319–328, March, 1972.

The author wishes to express his deep gratitude to V. B. Kudryavtsev for supervising the paper.

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Aleshin, S.V. Finite automata and Burnside's problem for periodic groups. Mathematical Notes of the Academy of Sciences of the USSR 11, 199–203 (1972). https://doi.org/10.1007/BF01098526

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