In [7], Tits classified spherical buildings of rank at least three. In the addenda of [7], he introduced the Moufang property for buildings and observed that with only the results of Chapter 4 of [7] one could show that an irreducible spherical building of rank at least three and all of its irreducible residues of rank at least two must satisfy the Moufang property. Tits and the author have rec...

A concept of the Moufang-Malt’tsev pair is elaborated. This concept is based on the generalized Maurer-Cartan equations of a local analytic Moufang loop. Triality can be seen as a fundamental property of such pairs. Based on triality, the Yamagutian is constructed. Properties of the Yamagutian are studied. 2000 MSC: 17D10

The differential equations for a local analytic Moufang loop are established. The commutation relations for the infinitesimal translations of the analytic Moufang are found. These commutation relations can be seen as a (minimal) generalization of the Maurer-Cartan equations. 2000 MSC: 20N05, 17D10

We continue the work by Aschbacher, Kinyon and Phillips [AKP] as well as of Glauberman [Glaub1,2] by describing the structure of the finite Bruck loops. We show essentially that a finite Bruck loop X is the direct product of a Bruck loop of odd order with either a soluble Bruck loop of 2-power order or a product of loops related to the groups P SL2(q), q = 9 or q ≥ 5 a Fermat prime. The latter ...

The first paper in this series initiated a study of Sylow theory for quasigroups and Latin squares, based on orbits of the left multiplication group. The current paper is based on socalled pseudo-orbits, which are formed by the images of a subset under the set of left translations. The two approaches agree for groups, but differ in the general case. Subsets are described as sectional if the pse...