On complemented non-abelian chief factors of Lie algebras

Ciloglu, Zekiye and Towers, David Anthony (2018) On complemented non-abelian chief factors of Lie algebras. Journal of Lie Theory, 28 (2). pp. 427-442. ISSN 0949-5932

Abstract

The number of Frattini chief factors or of chief factors which are complemented by a maximal subalgebra of a nite-dimensional Lie algebra L is the same in every chief series for L, by [13, Theorem 2.3]. However, this is not the case for the number of chief factors which are simply complemented in L. In this paper we determine the possible variation in that number.