# Right-transitively paranormal 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 **right-transitively paranormal** if every paranormal subgroup of the subgroup is paranormal in the whole group.

### Definition with symbols

A subgroup of a group is termed **right-transitively paranormal** in if whenever is a paranormal subgroup of , is also a paranormal subgroup of .

## Formalisms

### In terms of the right transiter

This property is obtained by applying the right transiter to the property: paranormal subgroup

View other properties obtained by applying the right transiter

## Relation with other properties

### Stronger properties

- Direct factor
- Central factor
- SCAB-subgroup
- Hereditarily normal subgroup
- Hereditarily pronormal subgroup
- Hereditarily paranormal subgroup

### Weaker properties

## Metaproperties

### Transitivity

This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitiveABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity

### 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