Geodesic
On Some Automorphisms of Orthogonal Groups in Odd Characteristic
Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 27-37.

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In this paper, it is proved that the simple orthogonal groups $O_{2n+1}(q)$ and $O_{2n}^\pm (q)$ (where $q$ is odd) cannot be automorphism groups of finite left distributive quasigroups. This is a particular case of the conjecture stating that the automorphism group of a left distributive quasigroup is solvable. To complete the proof of the conjecture, one must test all finite groups. 
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V. M. Galkin; N. V. Mokhnina. On Some Automorphisms of Orthogonal Groups in Odd Characteristic. Matematičeskie zametki, Tome 70 (2001) no. 1, pp. 27-37. http://geodesic.mathdoc.fr/item/MZM_2001_70_1_a3/

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