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arXiv · 1612.06521

Metacyclic groups as automorphism groups of compact Riemann surfaces

Andreas Schweizer
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Abstract

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

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Andreas Schweizer. 2017-03-25. Metacyclic groups as automorphism groups of compact Riemann surfaces. https://doi.org/10.1007/s10711-017-0239-8

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