Upward-closed subgroup property
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]
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 is termed upward-closed or sometimes right-hereditary if whenever ≤ ≤ are groups such that satisfies property in , then also satisfies property in .
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.