Geodesic
On Mikheev's construction of enveloping groups
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 245-252

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Mikheev, starting from a Moufang loop, constructed a groupoid and reported that this groupoid is in fact a group which, in an appropriate sense, is universal with respect to enveloping the Moufang loop. Later Grishkov and Zavarnitsine gave a complete proof of Mikheev's results. Here we give a direct and self-contained proof that Mikheev's groupoid is a group, in the process extending the result from Moufang loops to Bol loops.
Classification : 20N05
Keywords: Bol loop; Moufang loop; autotopism group; group with triality 
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Hall, J. I. On Mikheev's construction of enveloping groups. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 2, pp. 245-252. http://geodesic.mathdoc.fr/item/CMUC_2010__51_2_a8/