It is well known that a group which is the product of two supersoluble subgroups and is not supersoluble in general. Under suitable permutability conditions on and , we show that for any minimal normal subgroup both and are supersoluble. We then exploit this to establish some sufficient conditions for to be supersoluble.
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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. 413–425DOI 10.4171/RMI/395