Abstract
AbstractA classical result of Baer states that a finite group G which is the product of two normal supersoluble subgroups is supersoluble if and only if Gʹ is nilpotent. In this article, we show that if G = AB is the product of supersoluble (respectively, w-supersoluble) subgroups A and B, A is normal in G and B permutes with every maximal subgroup of each Sylow subgroup of A, then G is supersoluble (respectively, w-supersoluble), provided that Gʹ is nilpotent. We also investigate products of subgroups defined above when $ A\cap B=1 $ and obtain more general results.
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