Subgroup with self-normalizing normalizer

Symbol-free definition
A subgroup of a group is termed a subgroup with self-normalizing normalizer if its defining ingredient::normalizer in the whole group is a defining ingredient::self-normalizing subgroup of the whole group.

Stronger properties

 * Weaker than::Normal subgroup
 * Weaker than::Self-normalizing subgroup
 * Weaker than::Intermediately subnormal-to-normal subgroup:
 * Weaker than::Procharacteristic subgroup
 * Weaker than::Pronormal subgroup
 * Weaker than::Subgroup with abnormal normalizer
 * Weaker than::Weakly procharacteristic subgroup
 * Weaker than::Weakly pronormal subgroup
 * Weaker than::Subgroup with weakly abnormal normalizer
 * Weaker than::Paracharacteristic subgroup
 * Weaker than::Paranormal subgroup
 * Weaker than::Polycharacteristic subgroup
 * Weaker than::Polynormal subgroup

Opposite properties
A subgroup can have a self-normalizing normalizer and satisfy one of the properties below only if it is normal.


 * 2-hypernormalized subgroup: A subgroup whose normalizer is a normal subgroup.
 * Finitarily hypernormalized subgroup: A subgroup such that repeatedly taking normalizers reaches the whole group in finitely many steps.
 * Hypernormalized subgroup: A subgroup such that repeatedly taking normalizers reaches the whole group eventually (possibly, using a transfinite number of steps).

Incomparable properties

 * Subnormal subgroup
 * 2-subnormal subgroup: