We start by describing all the varieties of loops Q that can be defined by autotopisms αx, x ∈ Q, where αx is a composition of two triples, each of which becomes an autotopism when the element x belongs to one of the nuclei. In this way we obtain a unifying approach to Bol, Moufang, extra, Buchsteiner and conjugacy closed loops. We reprove some classical facts in a new way and show how Buchstei...

Moufang sets are split doubly transitive permutation groups, or equivalently, groups with a split BN-pair of rank one. In this paper, we study so-called special Moufang sets with abelian root groups, under the model-theoretic restriction that the groups have finite Morley rank. These groups have a natural base field, and we classify them under the additional assumption that the base field is in...