On the dimensions of the root groups of full subquadrangles of Moufang quadrangles arising from algebraic groups

摘要

Let Γ be a Moufang quadrangle arising from an algebraic group in the sense of Tits [4]. We call the pair (s,t) the dimensions of Γ if the root group of point-elations (respectively line-elations) has dimension s (respectively t). If (s, t) are the dimensions of Γ, and if (s, t') are the dimensions of a subquadrangle Γ', then we show that s + t' ≤ t. This generalizes a result of Thas [3] for finite quadrangles, and of Kramer and Van Maldeghem (in preparation) for compact topological quadrangles. The proof we present is a geometric one using the notion of a subtended ovoid.