# Automorph-join-closed subnormal 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

A subgroup of a group is termed **automorph-join-closed subnormal** if the join of any collection of subgroups that are automorphic to it (i.e., its images under automorphisms of the whole group) is a subnormal subgroup.

## Relation with other properties

### Stronger properties

### Weaker properties

- Conjugate-join-closed subnormal subgroup
- Finite-automorph-join-closed subnormal subgroup
- Finite-conjugate-join-closed subnormal subgroup

## Facts

- Any automorph-join-closed subnormal subgroup of a normal subgroup is conjugate-join-closed subnormal.
`For full proof, refer: Automorph-join-closed subnormal of normal implies conjugate-join-closed subnormal`