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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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