Algebraic properties of quadratic quaternary rings

A quadratic quaternary ring (abbreviated QQR) was defined for generalized quadrangles [1] as the analogue of a planar ternary ring (abbreviated PTR) for projective planes. To be useful, this algebraic structure should have nice properties whenever the generalized quadrangle has a large automorphism group. This interaction is described in this paper. Both authors are supported by the National Fund of Scientific Research Belgium (NFWO).