Upward-closed 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
This article is about a general term. A list of important particular cases (instances) is available at Category: Upward-closed subgroup properties


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

Definition

Symbol-free definition

A subgroup property is said to be upward-closed or sometimes, right-hereditary, if whenever a subgroup has the property in a group, every intermediate subgroup also has the property in the group.

Definition with symbols

A subgroup property p is termed upward-closed or sometimes right-hereditary if whenever GHK are groups such that G satisfies property p in K, then H also satisfies property p in K.

In terms of the upward closure operator

A subgroup property is upward-closed if and only if it is unchanged under application of the upward closure operator. The upward closure operator is an idempotent property operator for subgroup properties.

Relation with other metaproperties

Stronger metaproperties

Weaker metaproperties

Related metaproperties