This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
This subgroup property is a finitarily tautological subgroup property: when the ambient group is a finite group, the property is satisfied.
View other such subgroup properties
Definition with symbols
A subgroup of a group is termed elliptic if for any subgroup of , form an elliptic pair of subgroups. In other words, there exists an such that:
where each is written times.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|normal subgroup||Permutable subgroup|FULL LIST, MORE INFO|
|permutable subgroup||permutes with every subgroup|||FULL LIST, MORE INFO|
|subgroup of finite index||Subgroup of finite double coset index|FULL LIST, MORE INFO|