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A note on uncountable groups with modular subgroup lattice

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Abstract

The aim of this paper is to investigate the behaviour of uncountable groups of cardinality \({\aleph}\) in which all proper subgroups of cardinality \({\aleph}\) have modular subgroup lattice. It is proved here that the lattice of subgroups of such a group G is modular, provided that G has no infinite simple homomorphic images of cardinality \({\aleph}\). A corresponding result for groups whose proper subgroups of large cardinality are quasihamiltonian is also proved.

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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, Napoli, Italy

    Francesco de Giovanni & Marco Trombetti

Authors
  1. Francesco de Giovanni
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  2. Marco Trombetti
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Correspondence to Francesco de Giovanni.

Additional information

The authors are members of GNSAGA (INdAM), and work within the ADV-AGTA project.

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de Giovanni, F., Trombetti, M. A note on uncountable groups with modular subgroup lattice. Arch. Math. 107, 581–587 (2016). https://doi.org/10.1007/s00013-016-0964-5

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  • DOI: https://doi.org/10.1007/s00013-016-0964-5

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