Chevalley groups of type $G_2$ as automorphism groups of loops
| dc.creator | Vojtěchovský, Petr | |
| dc.date | 2007-01-24 | |
| dc.date.accessioned | 2026-07-07T07:42:51Z | |
| dc.date.available | 2026-07-07T07:42:51Z | |
| dc.description | Let $M^*(q)$ be the unique nonassociative finite simple Moufang loop constructed over $GF(q)$. We prove that $Aut(M^*(2))$ is the Chevalley group $G_2(2)$, by extending multiplicative automorphism of $M^*(2)$ into linear automorphisms of the unique split octonion algebra over GF(2). Many of our auxiliary results apply in the general case. In the course of the proof we show that every element of a split octonion algebra can be written as a sum of two elements of norm one. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701699 | |
| dc.identifier | http://arxiv.org/abs/math/0701699 | |
| dc.identifier | proceedings of Groups St Andrews 2001 in Oxford, Volume II, published in London Mathematical Society Lecture Note Series, 305, 586-598, Cambridge University Press, 2003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122601 | |
| dc.subject | Group Theory | |
| dc.subject | 20N05 | |
| dc.title | Chevalley groups of type $G_2$ as automorphism groups of loops | |
| dc.type | text |