JournalsrmiVol. 30, No. 2pp. 537–550

Groups with restrictions on subgroups of infinite rank

  • Maria De Falco

    Università degli Studi di Napoli Federico II, Italy
  • Francesco de Giovanni

    Università degli Studi di Napoli Federico II, Italy
  • Carmela Musella

    Università degli Studi di Napoli Federico II, Italy
  • Nadir Trabelsi

    Ferhat Abbas University, Setif, Algeria
Groups with restrictions  on subgroups of infinite rank cover

Abstract

It is known that a (generalized) soluble group whose proper subgroups of infinite rank are abelian either is abelian or has finite rank. It is proved here that if GG is a group of infinite rank such that all its proper subgroups of infinite rank have locally finite commutator subgroup, then the commutator subgroup GG' of GG is locally finite, provided that GG satisfies a suitable generalized solubility condition. Moreover, a similar result is obtained for groups whose proper subgroups of infinite rank are quasihamiltonian.

Cite this article

Maria De Falco, Francesco de Giovanni, Carmela Musella, Nadir Trabelsi, Groups with restrictions on subgroups of infinite rank. Rev. Mat. Iberoam. 30 (2014), no. 2, pp. 537–550

DOI 10.4171/RMI/792