Geodesic
On Moufang A-loops
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 2, pp. 371-375.

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In a series of papers from the 1940's and 1950's, R.H. Bruck and L.J. Paige developed a provocative line of research detailing the similarities between two important classes of loops: the diassociative A-loops and the Moufang loops ([1]). Though they did not publish any classification theorems, in 1958, Bruck's colleague, J.M. Osborn, managed to show that diassociative, commutative A-loops are Moufang ([5]). In [2] we relaunched this now over 50 year old program by examining conditions under which general --- not necessarily commutative --- diassociative A-loops are, in fact, Moufang. Here, we finish part of the program by characterizing Moufang A-loops. We also investigate simple diassociative A-loops as well as a class of centrally nilpotent diassociative A-loops. These results, {\it in toto}, reveal the distinguished positions two familiar classes of diassociative A-loops --- namely groups and commutative Moufang loops--play in the general theory.
Classification : 20N05
Keywords: diassociative; A-loop; Moufang 
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     title = {On {Moufang} {A-loops}},
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Phillips, J. D. On Moufang A-loops. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 2, pp. 371-375. http://geodesic.mathdoc.fr/item/CMUC_2000__41_2_a13/