# 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`