On derived length of the sum of two nilpotent Lie algebras (Q2768821)

The author studies Lie algebras over an arbitrary field which are decomposed into a sum \(L=A+B\) of two nilpotent subalgebras. It is shown that if \(A\) is abelian and \(B\) nilpotent of class 2 then the derived length of \(L\) does not exceed 10 over a field of \(\operatorname {char} \not= 2.\) Such solvable Lie algebras of arbitrary derived length \(\geq 2\) over any field of \(\operatorname {char} p= 2\) are built.