Abelian hereditarily normal subgroup
From Groupprops
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This article describes a property that arises as the conjunction of a subgroup property: hereditarily normal subgroup with a group property (itself viewed as a subgroup property): abelian group
View a complete list of such conjunctions
This article describes a property that arises as the conjunction of a subgroup property: transitively normal subgroup with a group property (itself viewed as a subgroup property): abelian group
View a complete list of such conjunctions
Definition
A subgroup H of a group G is termed an abelian hereditarily normal subgroup or abelian transitively normal subgroup of G if it satisfies the following equivalent conditions:
- H is abelian as a group and is a hereditarily normal subgroup of G.
- H is abelian as a group and is a transitively normal subgroup of G.
- H is an abelian normal subgroup of G and the induced action of the quotient group G / H on H is by power automorphisms.
Relation with other properties
Stronger properties
Weaker properties
