Proper normal subgroup

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This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: proper subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

Symbol-free definition

A subgroup of a group is termed a proper normal subgroup if it satisfies both these conditions:

Definition with symbols

A subgroup H of a group G is termed a proper normal subgroup if:

Relation with other properties

Stronger properties

Incomparable properties