Completing Segre’s proof of Wedderburn’s little theorem

bamberg, john; penttila, tim;

We use the Dandelin–Gallucci theorem to give a proof of Wedderburn’s little theorem that every finite division ring is commutative, and the proof is geometric in the sense that the non-geometric concepts employed are of an elementary nature. As a consequence, we obtain a geometric proof
that a finite Desarguesian projective space is Pappian.