  We introduce the product by generators of complex nilpotent Lie algebras,
which is a commutative product obtained from a central extension of the direct
sum of Lie algebras. We show that the product preserves also the characteristic
nilpotence provided that the multiplied algebras are $S$-algebras. In
particular, this shows the existence of nonsplit characteristically nilpotent
Lie algebras $\frak{h}$ such that the quotient $\frac{\dim \frak{h}-\dim
Z(\frak{h})}{\dim Z(\frak{h})} $ is as small as wanted.
