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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 2, pp. 371-389 (2000)
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Double Coverings and Reflexive Abelian Hypermaps

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Antonio J. Breda d'Azevedo, Gareth A. Jones

Departamento de Matematica, Universidade de Aveiro, 3800 Aveiro, Portugal; Department of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom

**Abstract:** We describe a general theory of hypermaps on surfaces, possibly non-orientable or with boundary. This includes techniques for constructing hypermaps as products and as double coverings, and for representing hypermaps as maps using homomorphisms between extended triangle groups. As a corollary we obtain a classification of the 16 reflexible hypermaps with abelian automorphism groups.

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