Function restriction-expressible subgroup property
From Groupprops
This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup propertyTemplate:Mapping system terminology
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]
Definition
Main definition
A subgroup property is said to be function restriction-expresssible if there exist function properties
and
such that
has a restriction formal expression
→
with respect to the function restriction formalism. In other words, a subgroup
satisfies
in a group
if and only if every function in
satisfying property
restricts to a function on
satisfying property
.
Relation with other metaproperties
Stronger metaproperties
- Invariance property: This is a subgroup property that can be expressed using the function restriction formalism with the right side being the property of just being a function.
- Balanced subgroup property: This is a subgroup property that can be expressed using the function restriction formalism with the left side and the right side being equal.
- Left-inner subgroup property
- Left-extensibility-stable subgroup property