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]

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.

Relation with other properties

Stronger properties

Weaker properties