Infinite groups with many permutable subgroups

  • Adolfo Ballester-Bolinches

    Universitat de València, Burjassot (Valencia), Spain
  • L. A. Kurdachenko

    National Dnepropetrovsk University, Ukraine
  • J. Otal

    Universidad de Zaragoza, Spain
  • T. Pedraza

    Universidad Politécnica de Valencia, Spain


A subgroup of a group is said to be permutable in , if for every subgroup of . A result due to Stonehewer asserts that every permutable subgroup is ascendant although the converse is false. In this paper we study some infinite groups whose ascendant subgroups are permutable (-groups). We show that the structure of radical hyperfinite -groups behave as that of finite soluble groups in which the relation to be a permutable subgroup is transitive (-groups).

Cite this article

Adolfo Ballester-Bolinches, L. A. Kurdachenko, J. Otal, T. Pedraza, Infinite groups with many permutable subgroups. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 745–764

DOI 10.4171/RMI/555