ON THE DIMENSIONS OF THE ROOT GROUPS OF FULL SUBQUADRANGLES OF MOUFANG QUADRANGLES ARISING FROM ALGEBRAIC-GROUPS

Let Gamma be a Moufang quadrangle arising from an algebraic group in t he sense of Tits [4]. We call the pair (s, t) the dimensions of Gamma if the root group of point-elations (respectively line-elations) has d imension 8 (respectively t). If (s, t) are the dimensions of Gamma, an d if (s, t') are the dimensions of a subquadrangle Gamma', then we sho w that s + t' less than or equal to t. This generalizes a result of Th as [3] for finite quadrangles, and of Kramer and Van Maldeghem tin pre paration) for compact topological quadrangles. The proof we present is a geometric one using the notion of a subtended ovoid.