In the present paper we generalize the concept of groups with triality and apply it to the theory of the Moufang, Bol and Bruck loops. Such generalizations allow us to reduce certain problems from the loop theory to problems ...

For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion for the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in the Moufang loops that do not possess p-Sylow ...

In this paper we construct a family of spin Lie groups G with an outer automorphism of order three (triality automorphism) and we describe the subgroups of fixed points for this kind of automorphisms. We will take advantage ...

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly ...

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly ...