Left-hereditary subgroup property

Symbol-free definition
A subgroup property is said to be left-hereditary if any subgroup of a subgroup having the property, also has the property.

Definition with symbols
A subgroup property $$p$$ is said to be left-hereditary if given groups $$G$$ &le; $$H$$ &le; $$K$$, such that $$H$$ satisfies property $$p$$ in $$K$$, $$G$$ also satisfies property $$p$$ in $$K$$.

In terms of the left transiter
A subgroup property is termed left-hereditary if its left transiter is the tautology.

Stronger metaproperties

 * Sub-functional subgroup property

Weaker metaproperties

 * Transitive subgroup property

Related metaproperties

 * Right-hereditary subgroup property
 * Upward-closed subgroup property
 * Intermediate subgroup condition