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
View other subgroup property conjunctions | view all subgroup properties

Definition

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

Relation with other properties

Stronger properties

Weaker properties