Function restriction-expressible 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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Definition

Main definition

A subgroup property $p$ is said to be function restriction-expresssible if there exist function properties $a$ and $b$ such that $p$ has a restriction formal expression $a$ → $b$ with respect to the function restriction formalism. In other words, a subgroup $H$ satisfies $p$ in a group $G$ if and only if every function in $G$ satisfying property $a$ restricts to a function on $H$ satisfying property $b$.

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