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Home > Vol 25, No 3 (2007)

Marston Conder¹ , Robert Jajcay² and Thomas Tucker³

¹University of Auckland Department of Mathematics Private Bag 92019 Auckland New Zealand Private Bag 92019 Auckland New Zealand
²Indiana State University Department of Mathematics and Computer Science Terre Haute IN 47809 USA Terre Haute IN 47809 USA
³Colgate University Mathematics Department Hamilton NY 13346 USA Hamilton NY 13346 USA

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.

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