A new characteristic subgroup of a p-stable group

We define a new non-identity characteristic subgroup, D⁎(S), of a finite p-group S, and prove that D⁎(S) is characteristic in a significant family of p-stable finite groups G having S as a Sylow p-subgroup. This result is analogous to an earlier result about ZJ(S) by the first author and has a very short proof.