BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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]
Definition with symbols
In other words, is the amalgam of with itself over , and is treated as the subgroup of given by the amalgamated between the two factors.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|normal subgroup||amalgam-characteristic implies normal||normal not implies amalgam-characteristic|||FULL LIST, MORE INFO|
- Characteristic subgroup: For full proof, refer: Characteristic not implies amalgam-characteristic Note that the other non-implication is clear from, for instance, finite normal implies amalgam-characteristic, because not every finite normal subgroup is characteristic (For full proof, refer: Normal not implies characteristic).