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Groups with finitely many normalizers of non-abelian subgroups

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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 commutator subgroup. Here the structure of locally graded groups with finitely many normalizers of (infinite) non-abelian subgroups is investigated, and the above result is extended to this more general situation.

Keywords: normalizer subgroup, metahamiltonian group

Mathematics Subject Classification (2000): 20F24

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I–80126 Napoli (Italy),  

    Fausto De Mari

  2. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I–80126 Napoli (Italy),  

    Francesco de Giovanni

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  1. Fausto De Mari
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  2. Francesco de Giovanni
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De Mari, F., de Giovanni, F. Groups with finitely many normalizers of non-abelian subgroups. Ricerche mat. 55, 151–157 (2006). https://doi.org/10.1007/s11587-006-0018-6

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  • DOI: https://doi.org/10.1007/s11587-006-0018-6

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