Groups with finitely many derived subgroups of non-normal subgroups |
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Authors: | Francesco de Mari Francesco de Giovanni |
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Affiliation: | (1) Dipartimento di Matematica e Applicazioni, Universitá di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I - 80126 Napoli, Italy |
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Abstract: | A group is called metahamiltonian if all its non-abelian subgroups are normal; it is known that locally soluble metahamiltonian groups have finite derived subgroup. This result is generalized here, by proving that every locally graded group with finitely many derived subgroups of non-normal subgroups has finite derived subgroup. Moreover, locally graded groups having only finitely many derived subgroups of infinite non-normal subgroups are completely described. Received: 25 April 2005 |
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Keywords: | 20F24 |
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