Subgroup contained in the Baer norm
From Groupprops
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Contents
Definition
A subgroup of a group is termed a subgroup contained in the Baer norm if it satisfies the following equivalent conditions:
- It is contained in the Baer norm of the whole group.
- It normalizes every subgroup of the whole group.
Formalisms
In terms of the subgroup-defining function containment operator
This property is obtained by applying the subgroup-defining function containment operator to the property: Baer norm
View other properties obtained by applying the subgroup-defining function containment operator
Relation with other properties
Weaker properties
- Permutable subgroup: Also related:
- 2-subnormal subgroup: Also related:
- Permutable 2-subnormal subgroup