  We look at simple groups associated primarily with the general theory of
Moufang buildings, and to analyze their relation to stability theory in the
model theoretic sense. As it becomes quite technical in the details, a lengthy
introduction surveys the developments at a less detailed level.
  The text, beginning from the second section, first deals with some model
theoretic algebra of fields, followed by an extended study of three associated
families of simple groups coming from the theory of Tits buildings, Moufang
polygons, and Timmesfeld's theory of exotic analogs of SL_2.
  The field theoretic part is fundamental ({\S}2). The rest of the paper
relates this to group theoretic constructions, with two sections surveying the
consequences for the original Tits and Timmesfeld theory before concentrating
on the more exotic groups associated with Moufang polygons.
  A good deal of the group theoretical material is expository, aimed to make
the relevant structural information meaningful to those coming from the
direction of model theory.
