# Intersection of automorph-conjugate subgroups

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

A subgroup of a group is termed an **intersection of automorph-conjugate subgroups** if it can be expressed as the intersection of (possibly infinitely many) automorph-conjugate subgroups.

## Formalisms

### In terms of the intersection-closure operator

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

View other properties obtained by applying the intersection-closure operator

## Relation with other properties

### Stronger properties

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

Characteristic subgroup | invariant under all automorphisms | Automorph-conjugate subgroup|FULL LIST, MORE INFO | ||

Automorph-conjugate subgroup | all automorphic subgroups are conjugate | |FULL LIST, MORE INFO |

### Weaker properties

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

Core-characteristic subgroup | its normal core is a characteristic subgroup | |FULL LIST, MORE INFO |