WNSCDIN-relatively weakly closed subgroup

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Definition

A subgroup $H$ of a group $K$ is termed WNSCDIN-relatively weakly closed in $K$ if whenever $K$ is embedded as a WNSCDIN-subgroup of $G$, $H$ is weakly closed in $K$ relative to $G$.

Relation with other properties

Stronger properties

• Isomorph-free subgroup
• Isomorph-normal characteristic subgroup: For full proof, refer: Isomorph-normal characteristic of WNSCDIN implies weakly closed

Weaker properties

• Left-transitively WNSCDIN-subgroup