Intersection of subnormal subgroups

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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]

Definition

A subgroup of a group is termed an intersection of subnormal subgroups if it satisfies the following equivalent conditions:

  • It can be expressed as the intersection of a descending chain of subnormal subgroups.
  • It can be expressed as an intersection of subnormal subgroups.

Note that since subnormality is finite-intersection-closed, and moreover, subnormality of fixed depth is closed under arbitrary intersections, these two definitions are equivalent.

Relation with other properties

Stronger properties

Weaker properties