Octonions, simple Moufang loops and triality

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Nonassociative finite simple Moufang loops are exactly the loops constructed by Paige from Zorn vector matrix algebras. We prove this result anew, using geometric loop theory. In order to make the paper accessible to a broader audience, we carefully discuss the connections between composition algebras, simple Moufang loops, simple Moufang 3-nets, $S$-simple groups and groups with triality. Related results on multiplication groups, automorphisms groups and generators of Paige loops are provided.
30 pages

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Group Theory, 20N05, 20D05

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http://salesiana.dossiersoluciones.com/handle/123456789/122607

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701707
 http://arxiv.org/abs/math/0701707
 proceedings of Workshops Loops '03, Prague, published in Quasigroups and Related Systems 10 (2003), 65-93

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arXiv