# Intersection-transitively automorph-conjugate subgroup

From Groupprops

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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 **intersection-transitively automorph-conjugate** if its intersection with any automorph-conjugate subgroup is again automorph-conjugate.

## Formalisms

### In terms of the intersection-transiter

This property is obtained by applying the intersection-transiter to the property: automorph-conjugate subgroup

View other properties obtained by applying the intersection-transiter

## Relation with other properties

### Stronger properties

- Characteristic subgroup:
*For proof of the implication, refer Characteristic implies intersection-transitively automorph-conjugate and for proof of its strictness (i.e. the reverse implication being false) refer Intersection-transitively automorph-conjugate not implies characteristic*.

### Weaker properties

## Metaproperties

### Intersection-closedness

YES:This subgroup property is intersection-closed: an arbitrary (nonempty) intersection of subgroups with this property, also has this property.ABOUT THIS PROPERTY: View variations of this property that are intersection-closed | View variations of this property that are not intersection-closedABOUT INTERSECTION-CLOSEDNESS: View all intersection-closed subgroup properties (or, strongly intersection-closed properties) | View all subgroup properties that are not intersection-closed | Read a survey article on proving intersection-closedness | Read a survey article on disproving intersection-closedness