# Intermediately automorph-conjugate subgroup

From Groupprops

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]

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

## Definition

### Symbol-free definition

A subgroup of a group is said to be **intermediately automorph-conjugate** if it is an automorph-conjugate subgroup in every intermediate subgroup (viz, every subgroup of the whole group containing it).

### Definition with symbols

A subgroup of a group is said to be **intermediately automorph-conjugate** if for any subgroup of such that , is an automorph-conjugate subgroup of . In other words, for any automorphism of , there exists such that .

## Formalisms

BEWARE!This section of the article uses terminology local to the wiki, possibly without giving a full explanation of the terminology used (though efforts have been made to clarify terminology as much as possible within the particular context)

### In terms of the intermediately operator

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

View other properties obtained by applying the intermediately operator

### In terms of the intermediately operator

This property is obtained by applying the intermediately operator to the property: weakly procharacteristic subgroup

View other properties obtained by applying the intermediately operator

## Relation with other properties

### Stronger properties

- Isomorph-free subgroup
- Intermediately isomorph-conjugate subgroup
- Intermediately characteristic subgroup
- Sylow subgroup