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Simple groups with infinite verbal width and the same positive theory as free groups

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Abstract

In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these simple groups have infinite w-verbal width for all proper words w.

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Authors and Affiliations

  1. Ikerbasque — Basque Foundation for Science, Sarriena s/n, 48940, Leioa - Bizkaia, Spain

    Montserrat Casals-Ruiz & Ilya Kazachkov

  2. Matematika Saila, UPV/EHU, Sarriena s/n, 48940, Leioa - Bizkaia, Spain

    Montserrat Casals-Ruiz, Albert Garreta, Ilya Kazachkov & Javier de la Nuez González

Authors
  1. Montserrat Casals-Ruiz
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  2. Albert Garreta
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  3. Ilya Kazachkov
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  4. Javier de la Nuez González
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Corresponding author

Correspondence to Ilya Kazachkov.

Additional information

The authors are supported by ERC grant PCG-336983, Basque Government Grant IT1483-22 and Spanish Government grants PID2019-107444GA-I00 and PID2020-117281GB-I00.

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Casals-Ruiz, M., Garreta, A., Kazachkov, I. et al. Simple groups with infinite verbal width and the same positive theory as free groups. Isr. J. Math. 254, 39–56 (2023). https://doi.org/10.1007/s11856-022-2384-5

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  • DOI: https://doi.org/10.1007/s11856-022-2384-5

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