2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156762Suppose that an automorphism group $G$ acts flag-transitively on a finite generalized hexagon or octagon $\cS$, and suppose that the action on both the point and line set is primitive. We show that $G$ is an almost simple group of Lie type, that is, the socle of $G$ is a simple Chevalley group.forgot to upload the appendices in version 1, and this is rectified in version 2. erased cross-ref keys in version 3. Minor revision in version 4 to implement the suggestion by the referee (new section at the end, extended acknowledgment, simpler proof for Lemma 4.2)CombinatoricsGroup Theory05B25,20B15, 20B25text