Chief factors covered by projectors of soluble Leibniz algebras

Abstract

Let F be a saturated formation of soluble Leibniz algebras. Let K be an F-projector and A/B a chief factor of the soluble Leibniz algebra L. It is well-known that if A/B is F-central, then K covers A/B. I prove the converse: if K covers A/B, then A/B is F-central.