# Semantic search

Abelian and pronormal implies SCDIN, Abnormal normalizer not implies pronormal, Center of pronormal subgroup is subset-conjugacy-determined in normalizer, Hall not implies pronormal, Intermediately isomorph-conjugate of normal implies pronormal, Join with any distinct conjugate is the whole group implies pronormal, Maximal implies pronormal, Nilpotent join of pronormal subgroups is pronormal, Normalizer of pronormal implies abnormal, Paranormal not implies pronormal, Procharacteristic of normal implies pronormal, Pronormal implies MWNSCDIN, Pronormal implies WNSCDIN, Pronormal implies intermediately subnormal-to-normal, Pronormal implies self-conjugate-permutable, Pronormal implies weakly closed in intermediate nilpotent, Pronormal implies weakly normal, Pronormal not implies NE, Pronormal not implies join with any distinct conjugate is the whole group, Pronormal subgroup is normal subset-conjugacy-determined in normalizer, Pronormality does not satisfy transfer condition, Pronormality is normalizer-closed, Pronormality is normalizing join-closed, Pronormality is not centralizer-closed, Pronormality is not commutator-closed, Pronormality is not finite-intersection-closed, Pronormality is not finite-join-closed, Pronormality is not finite-upper join-closed, Pronormality is not permuting join-closed, Pronormality is not transitive, Pronormality satisfies intermediate subgroup condition, Sylow implies pronormal, Sylow of normal implies pronormal, Weakly normal subgroup of symmetric group must move more than half the elements