Nilpotent automorphism groups of Riemann surfaces

Zomorrodian, Reza

doi:10.1090/S0002-9947-1985-0773059-6

Nilpotent automorphism groups of Riemann surfaces
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Trans. Amer. Math. Soc. 288 (1985), 241-255 Request permission

Abstract:

The action of nilpotent groups as automorphisms of compact Riemann surfaces is investigated. It is proved that the order of a nilpotent group of automorphisms of a surface of genus $g \geqslant 2$ cannot exceed $16(g - 1)$. Exact conditions of equality are obtained. This bound corresponds to a specific Fuchsian group given by the signature (0;2,4,8).

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Ueber die hyperelliptischen Curven und diejenigen vom Geschlechte

welche eindeutigen Transformationen in sich zulassen

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