Nilpotent Lie algebras in which all proper subalgebras have class at most \(n\) (Q2247749)

Let \(L\) be a finitely generated nilpotent Lie algebra over a field \(K\). Suppose that every proper subalgebra has class at most \(n\). Let \(d\) be the minimum number of elements that generate \(L\). Let \(q=\lfloor n/d-1 \rfloor\). It is shown that the class of \(L\) is at most \(n+q\). The main result is to show that there exist Lie algebras whose class meets this bound when \(K\) has characteristic \(0\) or is of prime characteristic \(p\) such that \(p\) does not divide \((q^2-1)q/2\).