Hsu, Tim Moufang loops of class 2 and cubic forms. (English) Zbl 0962.20046 Math. Proc. Camb. Philos. Soc. 128, No. 2, 197-222 (2000). The author shows that: – the nucleary-derived (normal associator) subloop of a Moufang loop of class \(p\) has exponent dividing 6. In particular, for \(p>3\) the subloop of elements of \(p\)-power order is associative; – if \(L\) is an SFML (small Frattini Moufang loop), \(Z\) its central subgroup of order \(p\), then \(L/Z\) has the structure of a vector space with a symplectic cubic form; – every symplectic cubic form is realized by some SFML; – two SFMLs are isomorphic iff their symplectic cubic spaces are isomorphic. Finally, many of these results are extended to all finite Moufang loops of class 2. Reviewer: Elena Brožíková (Praha) Cited in 11 Documents MSC: 20N05 Loops, quasigroups 11E76 Forms of degree higher than two Keywords:small Frattini Moufang loops; symplectic cubic forms; symplectic cubic spaces; finite Moufang loops PDFBibTeX XMLCite \textit{T. Hsu}, Math. Proc. Camb. Philos. Soc. 128, No. 2, 197--222 (2000; Zbl 0962.20046) Full Text: DOI