Geodesic
Classes of points of cubic hypersurfaces defined over finite fields
Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 121-130 Cet article a éte moissonné depuis la source Math-Net.Ru

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The points of a cubic hypersurface are divided into equivalence classes of Ya. I. Manin [1]. It is established that the quasigroup of these equivalence classes over a finite field is isomorphic to either 1 or $Z_2$ or $Z_3$ under some weak conditions. 
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     author = {D. S. Kanevskii},
     title = {Classes of points of cubic hypersurfaces defined over finite fields},
     journal = {Matemati\v{c}eskie zametki},
     pages = {121--130},
     year = {1976},
     volume = {20},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a12/}
}
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D. S. Kanevskii. Classes of points of cubic hypersurfaces defined over finite fields. Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 121-130. http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a12/