Left-extensibility-stable subgroup property
This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
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This subgroup metaproperty is related to, or can be defined, using the following formalism: function restriction formalism
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-extensibility-stable subgroup properties
Definition with symbols
A subgroup property is termed left-extensibility-stable if we can write:
where is an extensibility-stable function property.
The above symbols mean that:
- A subgroup has property in a group if and only if every function from to itself satisfying property restricts to a function from to itself satisfying property .
- Property being extensibility-stable means the following: whenever are groups,
and is a function on satisfying , then there is a function on satisfying such that the restriction of to is .
In terms of the left expressibility operator
Relation with other metaproperties
- Intermediate subgroup condition: For full proof, refer: Left-extensibility-stable implies intermediate subgroup condition