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Article

Drápal, Aleš
A-loops close to code loops are groups. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 41 (2000), issue 2, pp. 245-249
MSC: 20N05 | MR 1780868 | Zbl 1038.20046
Keywords:
A-loop; central nilpotency; Osborn problem
Summary:
Let $Q$ be a diassociative A-loop which is centrally nilpotent of class 2 and which is not a group. Then the factor over the centre cannot be an elementary abelian 2-group.
References:
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[3] Bruck R.H., Paige L.J.: Loops whose inner mappings are automorphisms. Ann. of Math. 63 (1954), 308-323. MR 0076779
[4] Chein O., Goodaire E.G.: Moufang loops with a unique non-identity commutator (associator, square). J. Algebra 130 (1990), 369-384. MR 1051308
[5] Griess R.L., Jr.: Code loops. J. Algebra 100 (1986), 224-234. MR 0839580 | Zbl 0589.20051
[6] Osborn M.J.: A theorem on A-loops. Proc. Amer. Math. Soc. 9 (1958), 347-349. MR 0093555 | Zbl 0097.25302
[7] Phillips J.D.: On Moufang A-loops. Comment. Math. Univ. Carolinae 41 (2000), 371-375. MR 1780878 | Zbl 1038.20050
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