The author characterizes the (perfect central extensions of the) little projective groups of the spherical Moufang buildings by means of the global commutation relations. More precisely, he presupposes the existence of subgroups (called `root groups') attached to the roots of a root system (irreducible with possibly multiple roots -- the cases \(BC_n\) and \(^2F_4\)) and requires that (1) the commutator of two root groups associated to roots which are not opposite in direction, lands inside the group generated by the root groups attached to the roots which are linear combinations of the two original roots with positive (but not necessarily integer) coefficients. Furthermore, (2) root groups associated to opposite equally long roots generate a rank 1 group (or split BN pair of rank 1 in a different terminology). At last, the third condition (3) basically says that the root groups are conjugated amongst themselves in a natural way by the elements of the rank 1 groups. The author also gives some alternative sufficient conditions to replace the third condition, of which he says that it is hard to control. The main idea here is to ask for equality in (1), when restricting the coefficients to integers. This way, some groups in low characteristic escape (the so-called groups of mixed type). Although the setting is quite geometric, the proofs are entirely group theoretic.