Abstract
The aim of this paper is to discuss groups G=HK=HA=KA with a triple factorisation as a product of two subgroups H and K and a nilpotent normal subgroup A. It is of interest to know whether such a group G satisfies some nilpotency or supersolubility condition if H and K satisfy the same condition. A positive answer to this problem is given for certain group classes under the hypothesis that A is prefactorised in G = HK. Some applications of the main theorem are also mentioned.
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