The centre of a finite semifield plane is a geometric invariant (Q1097510)

It is well known that the left, middle, and right nucleus, of a finite semifield are geometric invariants, that is, they do not change if the plane is recoordinatized by another semifield. On the other hand, the nucleus of the semified is in general not a geometric invariant. The authors now prove that the center (the subfield of central elements of the semifield) is a geometric invariant. The proof is not based on previous results about semifields obtained by the authors, because they feel that a self-contained spread-theoretic proof is more appropriate to their result.