Moufang loop multiplication groups with triality (Q1567156)

The author directly continues the work of \textit{G. Glauberman} [J. Algebra 8, 393-414 (1968; Zbl 0155.03901)] and \textit{S. Doro} [Math. Proc. Camb. Philos. Soc. 83, 377-392 (1978; Zbl 0381.20054)] which investigated a special automorphism of order three on the multiplication group of Moufang loops with trivial nucleus and a class of groups with a special automorphism of order three (so-called triality). This paper underlines the fundamental role played by commutative Moufang loops of exponent three and by Moufang loops with trivial nucleus in the general theory of Moufang loops.