Geodesic
The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 290-303 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that there are only finitely many symmetrical $2$-extensions of a locally finite graph whenever the automorphism group of the graph has an abelian subgroup of finite index (this case is of interest for certain applications). Some refinements and generalizations of this result are also given.
Keywords: graph, group of automorphisms, symmetrical extension of graphs. 
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V. I. Trofimov. The finiteness of the number of symmetrical 2-extensions of the $d$-dimensional lattice and similar graphs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 290-303. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a30/

[1] Trofimov V. I., “Symmetrical extensions of graphs and some other topics in graph theory related with group theory”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17, no. 4, 2011, 316–320

[2] Hall M., “A topology for free groups and related topics”, Ann. Math., 52 (1950), 127–139 | DOI | MR | Zbl