Groups with metamodular subgroup lattice

Volume 95 / 2003

M. De Falco, F. de Giovanni, C. Musella, R. Schmidt Colloquium Mathematicum 95 (2003), 231-240 MSC: Primary 20F24. DOI: 10.4064/cm95-2-7

Abstract

A group $G$ is called metamodular if for each subgroup $H$ of $G$ either the subgroup lattice ${{{\mathfrak L}}}(H)$ is modular or $H$ is a modular element of the lattice ${{{\mathfrak L}}}(G)$. Metamodular groups appear as the natural lattice analogues of groups in which every non-abelian subgroup is normal; these latter groups have been studied by Romalis and Sesekin, and here their results are extended to metamodular groups.

Authors

  • M. De FalcoDipartimento di Matematica e Applicazioni
    Università di Napoli
    via Cintia
    I-80126 Napoli, Italy
    e-mail
  • F. de GiovanniDipartimento di Matematica e Applicazioni
    Università di Napoli
    via Cintia
    I-80126 Napoli, Italy
    e-mail
  • C. MusellaDipartimento di Matematica e Applicazioni
    Università di Napoli
    via Cintia
    I-80126 Napoli, Italy
    e-mail
  • R. SchmidtMathematisches Seminar
    Universität Kiel
    Ludewig-Meyn-Str. 4
    D-24098 Kiel, Germany
    e-mail

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