Subgroup contained in the Baer norm

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]

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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:
  • Hereditarily permutable subgroup
  • Automorph-permutable subgroup
  • Conjugate-permutable subgroup
• 2-subnormal subgroup: Also related:
  • Normal subgroup of characteristic subgroup
  • Hereditarily 2-subnormal subgroup
  • Subnormal subgroup
  • Hereditarily subnormal subgroup
• Permutable 2-subnormal subgroup
  • Permutable subnormal subgroup