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.
@article{119170,
author = {Jon D. Phillips},
title = {On Moufang A-loops},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {41},
year = {2000},
pages = {371-375},
zbl = {1038.20050},
mrnumber = {1780878},
language = {en},
url = {http://dml.mathdoc.fr/item/119170}
}
Phillips, Jon D. On Moufang A-loops. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 371-375. http://gdmltest.u-ga.fr/item/119170/
Loops whose inner mappings are automorphisms, Ann. of Math. 63 (2) (1956), 308-232. (1956) | MR 0076779 | Zbl 0074.01701
On diassociative A-loops, submitted.
On loops of odd order II, J. Algebra 8 (1968), 393-414. (1968) | MR 0222198 | Zbl 0155.03901
Zur struktur von alternativkorpern, Math. Ann. 110 (1935), 416-430. (1935) | MR 1512948
A theorem on A-loops, Proc. Amer. Math. Soc. 9 (1959), 347-349. (1959) | MR 0093555