Geodesic
On the $\varphi$-structure on the projective group $L_2(q)$
Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 725-728 
S. V. Leshcheva; O. V. Suvorova. On the $\varphi$-structure on the projective group $L_2(q)$. Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 725-728. http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a10/
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     title = {On the $\varphi$-structure on the projective group $L_2(q)$},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper it is proved that the projective group $L_2(q)$ cannot be the automorphism group of a finite left distributive quasigroup. This is a special case of the conjecture according to which the automorphism group of a left distributive quasigroup is solvable.

[1] Galkin V. M., “Levodistributivnye kvazigruppy konechnogo poryadka”, Kvazigruppy i lupy, Kishinev, 1973

[2] Busarkin V. M., Gorchakov Yu. M., Konechnye rasscheplyaemye gruppy, Nauka, M., 1968

[3] Seminar po algebraicheskim gruppam, Mir, M., 1973

[4] Dedonne Zh., Geometriya klassicheskikh grupp, Mir, M., 1974

[5] Steinberg R., Lektsii po gruppam Shevalle, Mir, M., 1975 | Zbl