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

Abstract

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 $|G|\geqλ(g-1)$ for some real number $λ>6$, then for all sufficiently large $p$ (depending on $λ$), $\cal S$ and $G$ lie in one of six infinite sequences of examples. In particular, if $λ=8$ then this holds for all $p\geq 17$ and we obtain the largest groups of automorphisms of Riemann surfaces of genenera $g=p+1$.