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Gaps in probabilities of satisfying some commutator-like identities

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Abstract

We show that there is a positive constant δ < 1 such that the probability of satisfying either the 2-Engel identity [X1, X2, X2] = 1 or the metabelian identity [[X1, X2], [X3, X4]] = 1 in a finite group is either 1 or at most δ

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, University of Salerno, Via Giovanni Paolo II, 132, 84O84, Fisciano, Italy

    Costantino Delizia

  2. Departamento de Matemáticas, University of the Basque Country, Apartado 644, 48080, Bilbao, Spain

    Urban Jezernik

  3. Faculty of mathematics and physics, University of Ljubljana, Jadranska ulica 19, SI-1000, Ljubljana, Slovenia

    Primož Moravec

  4. Dipartimento di Matematica, University of Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, Italy

    Chiara Nicotera

Authors
  1. Costantino Delizia
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  2. Urban Jezernik
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  3. Primož Moravec
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  4. Chiara Nicotera
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Corresponding author

Correspondence to Urban Jezernik.

Additional information

The first and the fourth authors have been supported by the “National Group for Algebraic and Geometric Structures, and their Applications” (GNSAGA - INdAM).

The second author has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 748129. He has also been supported by the Spanish Government grant MTM2017-86802-P and by the Basque Government grant IT974-16.

The third author has been partially supported by the Slovenian Research Agency (research core funding No. P1-0222, and projects No. J1-8132, J1-7256 and N1-0061).

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Delizia, C., Jezernik, U., Moravec, P. et al. Gaps in probabilities of satisfying some commutator-like identities. Isr. J. Math. 237, 115–140 (2020). https://doi.org/10.1007/s11856-020-1999-7

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  • DOI: https://doi.org/10.1007/s11856-020-1999-7

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