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Some remarks on inp-minimal and finite burden groups

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Abstract

We prove that any left-ordered inp-minimal group is abelian and we provide an example of a non-abelian left-ordered group of dp-rank 2. Furthermore, we establish a necessary condition for a group to have finite burden involving normalizers of definable sets, reminiscent of other chain conditions for stable groups.

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Authors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds, UK

    Jan Dobrowolski

  2. Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia

    John Goodrick

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  1. Jan Dobrowolski
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  2. John Goodrick
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Correspondence to John Goodrick.

Additional information

Jan Dobrowolski was supported by Samsung Science Technology Foundation under Project No. SSTF-BA1301-03, and by European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 705410.

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Dobrowolski, J., Goodrick, J. Some remarks on inp-minimal and finite burden groups. Arch. Math. Logic 58, 267–274 (2019). https://doi.org/10.1007/s00153-018-0634-3

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  • DOI: https://doi.org/10.1007/s00153-018-0634-3

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