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Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 5, Pages 1142–1146 (Mi smj1796)  

This article is cited in 2 scientific papers (total in 2 papers)

Isomorphisms of Cayley graphs of a free Abelian group

A. A. Ryabchenko

Moscow Institute of Physics and Technology
Full-text PDF (285 kB) Citations (2)
References:
Abstract: A group $G$ is called a $CI$-group provided that the existence of some automorphism $\sigma\in\operatorname{Aut}(G)$, such that $\sigma(A)=B$ follows from an isomorphism $\operatorname{Cay}(G,A)\cong\operatorname{Cay}(G,B)$ between Cayley graphs, where $A$ and $B$ are two systems of generators for $G$. We prove that every finitely generated abelian group is a $CI$-group.
Keywords: abelian group, Cayley graph, distance graph.
Received: 05.09.2005
English version:
Siberian Mathematical Journal, 2007, Volume 48, Issue 5, Pages 919–922
DOI: https://doi.org/10.1007/s11202-007-0094-1
Bibliographic databases:
UDC: 512.541.52+519.175.1
Language: Russian
Citation: A. A. Ryabchenko, “Isomorphisms of Cayley graphs of a free Abelian group”, Sibirsk. Mat. Zh., 48:5 (2007), 1142–1146; Siberian Math. J., 48:5 (2007), 919–922
Citation in format AMSBIB
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\paper Isomorphisms of Cayley graphs of a~free Abelian group
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\yr 2007
\vol 48
\issue 5
\pages 1142--1146
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\transl
\jour Siberian Math. J.
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\crossref{https://doi.org/10.1007/s11202-007-0094-1}
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  • https://www.mathnet.ru/eng/smj/v48/i5/p1142
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Abstract page:330
    Full-text PDF :135
    References:38
     
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