Lazard derivation-invariant subgroup

Definition
Suppose $$G$$ is a defining ingredient::Lazard Lie group. A subgroup $$H$$ of $$G$$ is termed a Lazard derivation-invariant subgroup if $$H$$ is invariant under all the defining ingredient::Lazard derivations of $$G$$, i.e., all the functions from $$G$$ to itself that correpsond to defining ingredient::derivations of its Lazard Lie ring.