Left-hereditary subgroup property

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This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 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

Stronger metaproperties

Weaker metaproperties

Related metaproperties