# Intermediately join-transitively 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 **intermediately join-transitively subnormal** if it is a join-transitively subnormal subgroup inside every intermediate subgroup.

## Relation with other properties

### Stronger properties

Any property stronger than the property of being a join-transitively subnormal subgroup, that also satisfies the intermediate subgroup condition, is stronger than the property of being intermediately join-transitively subnormal.

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Join-transitively subnormal subgroup | ||||

Finite-automorph-join-closed subnormal subgroup | ||||

Finite-conjugate-join-closed subnormal subgroup | ||||

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