Automorphism groups of Riemann surfaces of genus p+1, where p is prime

Details Automorphism groups of Riemann surfaces of genus p+1, where p is prime Automorphism groups of Riemann surfaces of genus p+1, where p is prime

2003-06-05

arxiv.org/abs/math/0306106v2

Mathematics

Group Theory

16 pages, submitted to Galsgow Math. Journal

Scientific paper

We show that if $\cal S$ is a compact Riemann surface of genus $g = p+1$, where $p$ is prime, with a group of automorphisms $G$ such that $|G|\geq\lambda(g-1)$ for some real number $\lambda>6$, then for all sufficiently large $p$ (depending on $\lambda$), $\cal S$ and $G$ lie in one of six infinite sequences of examples. In particular, if $\lambda=8$ then this holds for all $p\geq 17$ and we obtain the largest groups of automorphisms of Riemann surfaces of genenera $g=p+1$.

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