# Conjugate-join-closed 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 **conjugate-join-closed subnormal** if the join of any collection of conjugate subgroups to it is a subnormal subgroup.

## Relation with other properties

### Stronger properties

### Weaker properties

- Join-transitively subnormal subgroup:
`For full proof, refer: Conjugate-join-closed subnormal implies join-transitively subnormal` - Intermediately join-transitively subnormal subgroup:
`For full proof, refer: Conjugate-join-closed subnormal implies intermediately join-transitively subnormal` - Finite-automorph-join-closed subnormal subgroup
- Finite-conjugate-join-closed subnormal subgroup

## Metaproperties

### Intermediate subgroup condition

YES:This subgroup property satisfies the intermediate subgroup condition: if a subgroup has the property in the whole group, it has the property in every intermediate subgroup.ABOUT THIS PROPERTY: View variations of this property satisfying intermediate subgroup condition | View variations of this property not satisfying intermediate subgroup conditionABOUT INTERMEDIATE SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition

If is a conjugate-join-closed subnormal subgroup of , and is an intermediate subgroup of containing , is also conjugate-join-closed subnormal in .