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On some permutable products of supersoluble groups.

Manuel J. AlejandreA. Ballester-BolinchesJohn CosseyM. C. Pedraza-Aguilera — 2004

Revista Matemática Iberoamericana

It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.

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