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Groupprops β

Left-hereditary subgroup property

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 GHK, 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