Single-input-expressible subgroup metaproperty

This article defines a subgroup metametaproperty
View a complete list of subgroup metametaproperties

Definition

A subgroup metaproperty $\alpha$ is termed single-input-expressible if it admits the following description. Consider a procedure $P$ that takes as input a pair of a group and a subgroup, and outputs a collection of group-subgroup pairs.

A subgroup property $p$ satisfies $\alpha$ if and only if, whenever the starting pair satisfies property $p$, all the pairs in the resulting collection also satisfy property $p$.

Relation with other metametaproperties

Weaker metaproperties

• Conjunction-closed subgroup metaproperty
• Disjunction-closed subgroup metaproperty
• Finite-input-expressible subgroup metaproperty