Automorphisms of \(F_4\) quadrangles (Q1434154)

The Moufang generalized quadrangles \(Q\) have been completely classified in [\textit{J. Tits} and \textit{R. Weiss}, Moufang polygons (Springer Monographs in Mathematics. Berlin: Springer) (2002; Zbl 1010.20017)] by using the group \(G^+\) generated by all root groups. The automorphism group \(G\) of \(Q\) contains \(G^+\) as a subgroup, and the structure of \(G\) has been completely studied only for some families. In this paper, the author proves that if \(Q\) is the Moufang generalized quadrangle related to buildings of type \(F_4,\) then its automorphism group is, up to field automorphisms, generated by the root group.