Geodesic
On symmetrical $q$-extensions of the 2-dimensional grid
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 199-209
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In the paper, properties of symmetrical $q$-extensions of the grids are investigated. We obtain a criteria for sets of symmetrical $q$-extensions of the grid $\Lambda^2$ to be finite. Using this criteria we prove, in particular, that the set of all $Aut_0(\Lambda^2)$-symmetrical $q$-extensions of the grid $\Lambda^2$ is finite for any prime $q$. In addition, we give a list of all $Aut_0(\Lambda^2)$-symmetrical 3-extensions of the grid $\Lambda^2$.
Keywords: $d$-dimensional grids, symmetrical $q$-extensions. 
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E. A. Neganova; V. I. Trofimov. On symmetrical $q$-extensions of the 2-dimensional grid. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 3, pp. 199-209. http://geodesic.mathdoc.fr/item/TIMM_2010_16_3_a21/

[1] Neganova E. A., Trofimov V. I., “O simmetricheskikh $q$-rasshireniyakh reshetok”, Teoriya grupp i ee prilozheniya, Tr. 8-i Mezhdunar. shk.-konf. po teorii grupp, posvyaschennoi 75-letiyu V. A. Belonogova, Nalchik, 2010, 186–189

[2] Neganova E. A., Trofimov V. I., “Simmetricheskie rasshireniya grafov”, Mezhdunar. algebr. konf., posvyaschennaya 70-letiyu A. V. Yakovleva, Tez. dokl., SPb., 2010, 51–53

[3] Seifter N., Trofimov V. I., “Automorphism Groups of Graphs with Quadratic Growth”, J. Comb. Theory. Ser. B, 71:2 (1997), 205–210 | DOI | MR | Zbl

[4] Neganova E. A., Trofimov V. I., “$Aut_0(\Lambda^d)$-simmetricheskie 2-rasshireniya reshetok $\Lambda^d$”, Problemy teoreticheskoi i prikladnoi matematiki, Tez. dokl. 41-i Vseros. mol. shk.-konf., Ekaterinburg, 2010, 64–70

[5] Trofimov V. I., “Ogranichennye avtomorfizmy grafov i odna kharakterizatsiya reshetok”, Izv. AN SSSR. Ser. matematicheskaya, 47:2 (1983), 407–420 | MR | Zbl