Join-transitively 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]

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Definition

Symbol-free definition

A subgroup of a group is termed join-transitively 2-subnormal if its join with any 2-subnormal subgroup is 2-subnormal.

Note that this is strictly stronger than the property of being 2-subnormal, because 2-subnormality is not finite-join-closed.

Formalisms

In terms of the join-transiter

This property is obtained by applying the join-transiter to the property: 2-subnormal subgroup
View other properties obtained by applying the join-transiter

Relation with other properties

Stronger properties

• Normal subgroup: For full proof, refer: Normal implies join-transitively 2-subnormal

Weaker properties

• 2-subnormal subgroup: Also related:
  • Join-transitively subnormal subgroup
  • Subnormal subgroup