Normal-hereditarily characteristic subgroup

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Definition

A subgroup of a group is termed a normal-hereditarily characteristic subgroup if every normal subgroup of the subgroup is a [[characteristic subgroup] of the whole group.

Relation with other properties

Stronger properties

• Characteristic subgroup which is a group in which every normal subgroup is characteristic
• Hereditarily characteristic subgroup

Weaker properties

• Characteristic subgroup
• Transitively normal subgroup
• Hereditarily normal-to-characteristic subgroup