A subgroup X of a group G is called pronormal-by-finite if there e- xistsapronormalsubgroupY ofGsuchthatY ≤X and|X :Y|isfinite.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, pro- vided that it has no infinite dihedral sections.

“Groups with all subgroups pronormal-by-finite ”

VINCENZI, Giovanni
2007-01-01

Abstract

A subgroup X of a group G is called pronormal-by-finite if there e- xistsapronormalsubgroupY ofGsuchthatY ≤X and|X :Y|isfinite.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, pro- vided that it has no infinite dihedral sections.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1656883
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