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Groups with All Subgroups Pronormal-by-Finite

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Abstract.

A subgroup X of a group G is called pronormal-by-finite if there exists a pronormal subgroup Y of G such that Y ≤ X and |X : Y| is finite. The structure of (generalized) soluble groups in which all subgroups are pronormal-by-finite is investigated. Among other results, it is proved in particular that a finitely generated soluble group with such property is central-by-finite, provided that it has no infinite dihedral sections.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo Via Cintia, I-80126, Napoli, Italy

    Francesco de Giovanni

  2. Dipartimento di Matematica, Seconda Università di Napoli, Via Vivaldi 43, I-81100, Caserta, Italy

    Alessio Russo

  3. Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte Don Melillo, I-84084, Fisciano, Salerno, Italy

    Giovanni Vincenzi

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  1. Francesco de Giovanni
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  2. Alessio Russo
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  3. Giovanni Vincenzi
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Correspondence to Francesco de Giovanni.

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de Giovanni, F., Russo, A. & Vincenzi, G. Groups with All Subgroups Pronormal-by-Finite. MedJM 4, 65–71 (2007). https://doi.org/10.1007/s00009-007-0103-4

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  • DOI: https://doi.org/10.1007/s00009-007-0103-4

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