Subalgebras that cover or avoid chief factors of Lie algebras

Towers, David (2015) Subalgebras that cover or avoid chief factors of Lie algebras. Proceedings of the American Mathematical Society, 143 (8). pp. 3377-3385. ISSN 0002-9939

Abstract

We call a subalgebra $U$ of a Lie algebra $L$ a $CAP$-subalgebra of $L$ if for any chief factor $H/K$ of $L$, we have $H \cap U = K \cap U$ or $H+U = K+U$. In this paper we investigate some properties of such subalgebras and obtain some characterizations for a finite-dimensional Lie algebra $L$ to be solvable under the assumption that some of its maximal subalgebras or $2$-maximal subalgebras be $CAP$-subalgebras.