ON DETERMINATION OF THE MINIMUM GENUS OF COMPACT RIEMANN SURFACES ADMITTING A CLASS OF METACYCLIC AUTOMORPHISM GROUPS

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Abstract

Every finite group can be represented as a group of automorphisms of a compact Riemann surface of genus g ≥ 2. It is of interest to determine the minimum genus of the Riemann surface on which a given finite group acts as a group of automorphisms.

Keywords and Phrases

Riemann surface, Fuchsian group, automorphism, epimorphism, smooth quotient, metacyclic group, genus.

A.M.S. subject classification

29H10, 30F35.

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