Proper normal subgroup
From Groupprops
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:
- It is a proper subgroup i.e. it is not the whole group
- It is a normal subgroup
Definition with symbols
A subgroup of a group
is termed a proper normal subgroup if:
-
i.e.
is not the whole of
-
i.e.
is a normal subgroup of