On some permutable products of supersoluble groups

  • Manuel J. Alejandre

    Universidad Miguel Hernández, Elche, Spain
  • Adolfo Ballester-Bolinches

    Universitat de València, Burjassot (Valencia), Spain
  • John Cossey

    Australian National University, Canberra, Australia
  • Mari Carmen Pedraza-Aguilera

    Universidad Politecnia de Valencia, Spain


It is well known that a group G=ABG = AB which is the product of two supersoluble subgroups AA and BB is not supersoluble in general. Under suitable permutability conditions on AA and BB, we show that for any minimal normal subgroup NN both ANAN and BNBN are supersoluble. We then exploit this to establish some sufficient conditions for GG to be supersoluble.

Cite this article

Manuel J. Alejandre, Adolfo Ballester-Bolinches, John Cossey, Mari Carmen Pedraza-Aguilera, On some permutable products of supersoluble groups. Rev. Mat. Iberoam. 20 (2004), no. 2, pp. 413–425

DOI 10.4171/RMI/395