  A 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 $
G' $ 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 $, $ B $ permutes with every maximal subgroup of each Sylow
subgroup of $ A $, then $ G $ is supersoluble (respectively, $ w
$-supersoluble) provided that $ G' $ is nilpotent. We also investigate products
of subgroups defined above when $ A\cap B=1 $ and obtain more general results.
