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
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.File in questo prodotto:
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