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.