Subnormal subalgebras of Leibniz algebras

Abstract

Zassenhaus has proved that if U is a subnormal subalgebra of a finite-dimensional Lie algebra L and V is a finite-dimensional irreducible L-module, then all U-module composition factors of V are isomorphic. Schenkman has proved that if U is a subnormal subalgebra of a finite-dimensional Lie algebra L, then the nilpotent residual of U is an ideal of L. These useful results generalise to Leibniz algebras.