We introduce the Profinite Hull functor of special groups, showing that it gives rise to a new local - global principle, the subform reflection property. We also indicate applications of this principle to the abstract algebraic theory of quadratic forms.

N₀-stable N₀-categorical linked quaternionic mappings are studied and are shown to correspond (in some sense) to special groups which are N₀-stable. N₀-categorical, satisfy AP(3) and have finite 2-symbol length. They are also related to special groups whose isometry relation is a finite union of cosets, which are then considered on their own, as well as their links with pseudofinite, profinite and weakly normal special groups.