Characteristic subgroup of additive group of a Lie ring

=Definition

Suppose $L$ is a Lie ring and $S$ is a subset of $L$. We say that $S$ is a characteristic subgroup of (the) additive group of $L$ if $S$ is a characteristic subgroup of the abelian group defined as the underlying additive group of $L$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
fully invariant subgroup of additive group of a Lie ring				|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
subgroup of additive group of a Lie ring				|FULL LIST, MORE INFO