Dedekind normal subgroup
From Groupprops
This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): Dedekind group
View a complete list of such conjunctions
Contents
Definition
A subgroup of a group is termed a Dedekind normal subgroup if it satisfies the following two conditions:
- It is a normal subgroup of the group.
- It is a Dedekind group: every subgroup of it is normal in it.
Relation with other properties
Stronger properties
- Central subgroup
- Cyclic normal subgroup
- Abelian normal subgroup
- Hereditarily normal subgroup
- Subgroup contained in the Baer norm
