Upward-closed 2-subnormal subgroup

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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 upward-closed 2-subnormal if every subgroup of the group containing it is a 2-subnormal subgroup of the whole group.

Definition with symbols

A subgroup H of a group G is termed an upward-closed 2-subnormal subgroup of G if whenever H \le K \le G, K is a 2-subnormal subgroup of G.

Relation with other properties

Stronger properties

Weaker properties