On groups with root system of type G2

Let Φ be a root system of type G2, and let G be a group generated by non-trivial subgroups Aα, α∈Φ, satisfying some generalized Steinberg relations, which are also satisfied by root subgroups corresponding to a Moufang hexagon. 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 G2 is provided. As a main result we classify the possible structures for G.