Properties of a finite group representable as the product of two nilpotent groups (Q2754822)

The author studies finite groups \(G=AB\), where \(A\) and \(B\) are nilpotent subgroups. The main theorem gives some properties of the factor-group \(G/F(G)\) (\(F(G)\) is the Fitting subgroup of \(G\), i.e. the product of all normal nilpotent subgroups of \(G\)). In particular, it is shown that the nilpotent coradical of the group \(G/F(G)\) coincides with the subgroup \([A,B]F(G)/F(G)\) and the intersection \(A\cap B\) is contained in \(H=[A,B]F(G)\) (the last normal subgroup can be written in the form \(H=(H\cap A)(H\cap B)\)).