# Normal subgroup in which every subgroup characteristic in the whole group is characteristic

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: normal subgroup and subgroup in which every subgroup characteristic in the whole group is characteristic

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## Definition

A subgroup of a group is termed a **normal subgroup in which every subgroup characteristic in the whole group is characteristic** if is a normal subgroup of and every subgroup of that is a characteristic subgroup of is also a characteristic subgroup of .