Join-transitively 2-subnormal subgroup
From Groupprops
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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
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