Weak normal subset-conjugacy-determined subgroup

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Weak normal subset-conjugacy-determined subgroup, all facts related to Weak normal subset-conjugacy-determined subgroup) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.
View other such properties

Definition

Suppose $H\leq K\leq G$. We say that $H$ if weak normal subset-conjugacy-determined in $K$ relative to $G$ if, for any normal subsets $A,B\subseteq H$ such that there exists $g\in G$ with $gAg^{-1}=B$, there exists $k\in K$ such that $kAk^{-1}=B$.

The modifier weak here denotes that $g$ and $k$ may not have the same element-wise action on $A$.

Relation with other properties

Stronger properties

• Normal subset-conjugacy-determined subgroup
• Subset-conjugacy-determined subgroup

Related subgroup properties

• WNSCDIN-subgroup: A subgroup that is weak normal subset-conjugacy-determined inside its normalizer.