On Groups with all Subgroups Subnormal

Name: On Groups with all Subgroups Subnormal
Creator: Casolo, Carlo
Keywords: soluble groups, Generalizations of solvable and nilpotent groups, Chains and lattices of subgroups, subnormal subgroups, 0101 mathematics, hyperabelian, 01 natural sciences, subnormal subgroups

Casolo, Carlo

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Bulletin of the Lond...arrow_drop_down

Bulletin of the London Mathematical Society

Article . 1985 . Peer-reviewed

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On Groups with all Subgroups Subnormal

On groups with all subgroups subnormal

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1985 English Publisher:WileyJournal:Bulletin of the London Mathematical Society, volume 17, pages 397-397 (issn: 0024-6093,

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Authors: Casolo, Carlo;

doi: 10.1112/blms/17.4.397

On Groups with all Subgroups Subnormal

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Abstract

It seems to be unknown whether every group G which has all its subgroups subnormal is soluble. Here it is shown that every such group G in which no nontrivial section is perfect, is hyperabelian and hence (by a result of Brookes) soluble.

Keywords

soluble groups, Generalizations of solvable and nilpotent groups, Chains and lattices of subgroups, subnormal subgroups, hyperabelian, subnormal subgroups

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