## Revista Matemática Iberoamericana

### On uniqueness of automorphisms groups of Riemann surfaces

#### Abstract

Let $\gamma, r, s$, $\geq 1$ be non-negative integers. If $p$ is a prime sufficiently large relative to the values $\gamma$, $r$ and $s$, then a group $H$ of conformal automorphisms of a closed Riemann surface $S$ of order $p^{s}$ so that $S/H$ has signature $(\gamma,r)$ is the unique such subgroup in $\mathrm{Aut}(S)$. Explicit sharp lower bounds for $p$ in the case $(\gamma,r,s) \in \{(1,2,1),(0,4,1)\}$ are provided. Some consequences are also derived.

#### Article information

Source
Rev. Mat. Iberoamericana, Volume 23, Number 3 (2007), 793-810.

Dates
First available in Project Euclid: 27 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1204128300

Mathematical Reviews number (MathSciNet)
MR2414492

Zentralblatt MATH identifier
1144.30017

#### Citation

Leyton A. , Maximiliano; Hidalgo, Rubén A. On uniqueness of automorphisms groups of Riemann surfaces. Rev. Mat. Iberoamericana 23 (2007), no. 3, 793--810. https://projecteuclid.org/euclid.rmi/1204128300

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