Displaying similar documents to “Commutative Moufang loops and distributive groupoids of small orders”

On Mikheev's construction of enveloping groups

J. I. Hall (2010)

Commentationes Mathematicae Universitatis Carolinae

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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.