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The finiteness of the number of symmetrical 2-extensions of the d-dimensional grid and similar graphs

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Abstract

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 obtained.

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References

  1. V. I. Trofimov, “Symmetrical extensions of the graphs and some other topics in graph theory related with group theory,” Proc. Steklov Inst. Math. 279(Suppl. 1), S107–S112 (2012).

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

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    V. I. Trofimov

  2. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina 51, Yekaterinburg, 620000, Russia

    V. I. Trofimov

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  1. V. I. Trofimov
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Correspondence to V. I. Trofimov.

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Original Russian Text © V.I. Trofimov, 2013, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Vol. 19, No. 3.

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Trofimov, V.I. The finiteness of the number of symmetrical 2-extensions of the d-dimensional grid and similar graphs. Proc. Steklov Inst. Math. 285 (Suppl 1), 169–182 (2014). https://doi.org/10.1134/S0081543814050198

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  • DOI: https://doi.org/10.1134/S0081543814050198

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