Normal subset-conjugacy-closed 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 normal subset-conjugacy-closed subgroup if it is a normal subset-conjugacy-determined subgroup in itself relative to the whole group.

Definition with symbols

A subgroup $H$ of a group $G$ is termed a normal subset-conjugacy-closed subgroup in $G$ if for any two normal subsets $A,B$ of $H$ such that there exists $g\in G$ with $gAg^{-1}=B$ , then $A=B$ .