Resumen de Cyclic groups of automorphisms of schottky type

Rubén Antonio Hidalgo

• Given an abstract group of orden n, we call its Schottky genus to the minimum genus ɡ ≥ 2 on which it acts as group of conformal automorphisms of Schottky type. In this note, we compute the Schottky genus for both cyclic and dihedral groups. In particular, we obtain that the Schottky genus of the dihedral group of order 2n is the same as for the cyclic group of order n. Since every dihedral group is of Schottky type, we have that the Schottky genus of a dihedral group of order 2n is also its minimum genus.