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A note on groups of infinite rank whose proper subgroups are abelian-by-finite

Volume 137 / 2014

Francesco de Giovanni, Federica Saccomanno Colloquium Mathematicum 137 (2014), 165-170 MSC: Primary 20F22. DOI: 10.4064/cm137-2-2

Abstract

It is proved that if $G$ is a locally (soluble-by-finite) group of infinite rank in which every proper subgroup of infinite rank contains an abelian subgroup of finite index, then all proper subgroups of $G$ are abelian-by-finite.

Authors

  • Francesco de GiovanniDipartimento di Matematica e Applicazioni
    Università degli Studi di Napoli “Federico II”
    80126 Napoli, Italy
    e-mail
  • Federica SaccomannoDipartimento di Matematica e Applicazioni
    Università degli Studi di Napoli “Federico II”
    80126 Napoli, Italy
    e-mail

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