On Bruck loops of 2-power exponent

The goal of this paper is two-fold. First we provide the information needed to study Bol, Ar or Bruck loops by applying group theoretic methods. This information is used in this paper as well as in Baumeister and Stein (2010) [BS3] and in Stein (2009) [S].Moreover, we determine the groups associated to Bruck loops of 2-power exponent under the assumption that every non-abelian simple group S is either passive or isomorphic to PSL2(q), q−1⩾4 a 2-power. In a separate paper it is proven that indeed every non-abelian simple group S is either passive or isomorphic to PSL2(q), q−1⩾4 a 2-power (Stein, 2009) [S]. The results obtained here are used in Baumeister and Stein (2010) [BS3], where we determine the structure of the groups associated to the finite Bruck loops.