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
Relation with other properties
- Regular retract
- Self-normalizing subgroup if nontrivial: For full proof, refer: Free factor implies self-normalizing or trivial
This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity
Counterexamples it gives
Self-normalizing subgroups that are not contranormal
A free factor is self-normalizing, but no nontrivial free factor is contranormal. This gives an example of a subgroup that is self-normalizing but not contranormal.