On series of Lie algebras of derivation (Q1127556)

The famous derivation tower theorem of \textit{E. Schenkman} [Am. J. Math. 73, 453-474 (1951; Zbl 0054.01804)] asserts that the derivation tower of a finite-dimensional Lie algebra with center \(O\) terminates in a complete Lie algebra after finitely many steps. The author investigates the structure of this terminal member. Then he considers Lie algebras in which each member of the derivation has non-zero center. If there is a bound on the dimensions of the members in the derivation tower, then the tower terminates in the direct sum of the ground field and a complete Lie algebra which is equal to its derived algebra.