Left-hereditary subgroup property

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
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This article is about a general term. A list of important particular cases (instances) is available at Category: Left-hereditary subgroup properties

Definition

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 $G$ ≤ $H$ ≤ $K$ , 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.

Relation with other metaproperties

Stronger metaproperties

Sub-functional subgroup property

Weaker metaproperties

Transitive subgroup property

Related metaproperties