WNSCC-subgroup

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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]

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Definition

Symbol-free definition

A subgroup of a group is termed a WNSCC-subgroup, or a weak normal subset-conjugacy-closed subgroup, if it is weak normal subset-conjugacy-determined in itself, relative to the whole group.

Definition with symbols

A subgroup $H$ of a group $G$ is termed a WNSCC-subgroup or weak normal subset-conjugacy-closed subgroup in $G$ if it satisfies the following condition: For any two normal subsets $A,B$ of $H$ such that there exists $g\in G$ with $gA{g}^{-1}=B$, we have $A=B$.

Relation with other properties

Stronger properties

• Abnormal subgroup: For full proof, refer: Abnormal implies WNSCC
• Direct factor
• Central factor
• Retract
• Subset-conjugacy-closed subgroup
• Normal subset-conjugacy-closed subgroup

Weaker properties

• WNSCDIN-subgroup