On the product by generators of characteristically nilpotent Lie \(S\)-algebras. (Q1410960)

The authors prove that the product of generators preserves the characteristic nilpotence of Lie algebras, provided that the multiplied algebras belong to the class of \(S\)-algebras. This shows the existence of nonsplit characteristically nilpotent Lie algebras \({\mathcal H}\) such that \((\dim{\mathcal H}- \dim Z({\mathcal H}))/\dim Z({\mathcal H})\) is as small as possible, where \(Z({\mathcal H})\) is the center of \({\mathcal H}\).