Geodesic
On the $\varphi$-structure on the projective group $L_2(q)$
Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 725-728.

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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. 
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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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