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N-barely transitive permutation groups

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Abstract

A group G is an N-barely transitive group (NBT-group) if G acts on an infinite set transitively and faithfully and all proper normal subgroups of G have finite orbits. We investigate the main properties and structure of NBT-groups. We give some examples in non-perfect and perfect case. Also we show that there does not exist a locally soluble perfect cofinitary NBT-group.

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Authors and Affiliations

  1. Science Faculty, Department of Mathematics, Gazi University, 06500, Teknikokullar, Ankara, Turkey

    Oğuz Alkış & Aynur Arıkan

  2. Gazi Education Faculty, Department of Mathematics and Science Education, Gazi University, 06500, Teknikokullar, Ankara, Turkey

    Ahmet Arıkan

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  1. Oğuz Alkış
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  2. Ahmet Arıkan
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  3. Aynur Arıkan
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Correspondence to Oğuz Alkış.

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Alkış, O., Arıkan, A. & Arıkan, A. N-barely transitive permutation groups. Ricerche mat 72, 141–152 (2023). https://doi.org/10.1007/s11587-021-00608-x

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  • DOI: https://doi.org/10.1007/s11587-021-00608-x

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