Strong containment of saturated formations of soluble Lie algebras

TL;DR

This paper investigates the structure of saturated formations of soluble Lie algebras, revealing conditions under which one formation strongly contains another and characterizing the formation generated by certain quotients.

Contribution

It establishes a characterization of saturated formations with strong containment and shows such formations are not locally defined, advancing the understanding of their structural properties.

Findings

H coincides with the formation generated by L/N(L) for L in H

H is not locally defined

Conditions for strong containment of saturated formations

Abstract

It is shown that, if H,K are saturated formations of soluble Lie algebras over a field of non-zero characteristic and H strongly contains K non-trivially, then H coincides with the formation generated by the L/N(L) for L in H, and that H is not locally defined.