Riemann surfaces and restrictively-marked hypermaps

Antonio Breda d'Azevedo

Abstract


If S is a compact Riemann surface of genus g > 1 then S has at most 84(g − 1) (orientation preserving) automorphisms (Hurwitz). On the other hand, if G is a group of automorphisms of S and |G| > 24(g − 1) then G is the automorphism group of a regular oriented map (of genus g) and if |G| > 12(g − 1) then G is the automorphism group of a regular oriented hypermap of genus g (Singerman). We generalise these results and prove that if |G| > g − 1 then G is the automorphism group of a regular restrictedly-marked hypermap of genus g. As a special case we also show that a marked finite transitive permutation group (Singerman) is a restrictedly-marked hypermap with the same genus.

Keywords


Groups, Riemann surface, hypermaps, maps, restrictedly-marked, restrictedly regular

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DOI: https://doi.org/10.26493/1855-3974.40.2ee

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications