# Series-equivalent not implies automorphic

From Groupprops

## Statement

It is possible to have a group and normal subgroups and of that are Series-equivalent subgroups (?) in the sense that and , but and are not automorphic subgroups -- in other words, there is no automorphism of that sends to .

## Related facts

### Stronger facts

There are many slight strengthenings of the result that are presented below, along with the smallest order of known examples.

## Proof

For the proof, see any of the stronger facts listed above.