Geodesic
Regular Cayley maps for finite abelian groups
Journal of Algebraic Combinatorics, Tome 25 (2007) no. 3, pp. 259-283.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A regular Cayley map for a finite group $A$ is an orientable map whose orientation-preserving automorphism group $G$ acts regularly on the directed edge set and has a subgroup isomorphic to $A$ that acts regularly on the vertex set. This paper considers the problem of determining which abelian groups have regular Cayley maps. The analysis is purely algebraic, involving the structure of the canonical form for $A$. The case when $A$ is normal in $G$ involves the relationship between the rank of $A$ and the exponent of the automorphism group of $A$, and the general case uses Ito's theorem to analyze the factorization $G = AY$, where $Y$ is the (cyclic) stabilizer of a vertex.
Keywords: keywords regular map, Cayley graph, abelian group 
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     title = {Regular {Cayley} maps for finite abelian groups},
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Conder, Marston; Jajcay, Robert; Tucker, Thomas. Regular Cayley maps for finite abelian groups. Journal of Algebraic Combinatorics, Tome 25 (2007) no. 3, pp. 259-283. http://geodesic.mathdoc.fr/item/JAC_2007__25_3_a3/