Quadratic pairs without commuting root-subgroups

Suppose G is a subgroup of GL(k), M a finite-dimensional vectorspace over the field k with char k≠2, generated by quadratic elements σ satisfying c○σ∈G for all c∈k∗. Then one can define root-subgroups of G intrinsically, i.e. just in terms of the quadratic elements.In this paper we determine such groups G generated by three root-subgroups, which do not contain a pair of commuting root-subgroups. This is a further step of the determination of groups G, when (G,M) is a quadratic pair.