Subring of a Lie ring that is maximal as a subgroup

This article describes a Lie subring property: a property that can be evaluated for a subring of a Lie ring
View a complete list of such properties
VIEW RELATED: Lie subring property implications | Lie subring property non-implications | Lie subring metaproperty satisfactions | Lie subring metaproperty dissatisfactions | Lie subring property satisfactions |Lie subring property dissatisfactions

Definition

Let $L$ be a Lie ring and $S$ be a subring of $L$. We say that $S$ is maximal as a subgroup if the additive group of $S$ is a maximal subgroup of the additive group of $L$.

Relation with other properties

Weaker properties

• Lie subring whose sum with any subring is a subring
• Maximal Lie subring