Metacyclic groups as automorphism groups of compact Riemann surfaces

Abstract

Let $X$ be a compact Riemann surface of genus $g\ge 2$, and let $G$ be a subgroup of $Aut(X)$. We show that if the Sylow $2$-subgroups of $G$ are cyclic, then $|G|\le 30(g-1)$. If all Sylow subgroups of $G$ are cyclic, then, with two exceptions, $|G|\le 10(g-1)$. More generally, if $G$ is metacyclic, then, with one exception, $|G|\le 12(g-1)$. Each of these bounds is attained for infinitely many values of $g$.

16 pages, final version, some improvements

References in corpus (1)

• On the exponent of the automorphism group of a compact Riemann surface

Cited by in corpus (1)

• Nilpotent groups of automorphisms of families of Riemann surfaces