Subgroups of the Chevalley groups of type F4 arising from a polar space

For any field K, we determine the quasi-simple subgroups G of the Chevalley group F4ðKÞ which are generated by a class S of so-called abstract transvection subgroups of G such that any member of S is contained in a long root subgroup of F4ðKÞ. First, we construct a polar space with point set S, which is embedded in the F4-geometry. This yields that a conjugate of G is contained in a classical standard subsystem subgroup of F4ðKÞ or G arises from a Moufang quadrangle in characteristic 2. For the second possibility, the so-called F4quadrangles are worth mentioning.