WNSCDIN-subgroup

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Definition

A subgroup of a group is termed a WNSCDIN-subgroup if it is a weak normal subset-conjugacy-determined subgroup inside its normalizer relative to the whole group.

Relation with other properties

Stronger properties

• Pronormal subgroup: For full proof, refer: Pronormal implies WNSCDIN

Weaker properties

• Subgroup in which every normalizer-relatively normal conjugation-invariantly relatively normal subgroup is weakly closed: For full proof, refer: WNSCDIN implies every normalizer-relatively normal conjugation-invariantly relatively normal subgroup is weakly closed