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 HH of a group GG is said to be \textit{permutable in GG}, if HK=KHHK = KH for every subgroup KK of GG. 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 (APAP--groups). We show that the structure of radical hyperfinite APAP--groups behave as that of finite soluble groups in which the relation \textit{to be a permutable subgroup} is transitive (PTPT--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