On Groups with Root System of Type 2 F 4

Let Φ̃ be a root system of type F4, and let G be a group generated by non-trivial subgroups Ar, r ∈ Φ̃, satisfying some generalized Steinberg relations, which are also satisfied by root subgroups corresponding to a Moufang octagon. These relations can be considered as a generalization of the element-wise commutator relations in Chevalley groups. The Steinberg presentation specifies the groups satisfying the Chevalley commutator relations. In the present paper some sort of generalized Steinberg presentation for groups with root system of type F4 is provided. As a main result we classify the possible structures of G.