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

Abstract

Let $X$ be a compact Riemann surface of genus $g\ge 2$, and let $Aut(X)$ be its group of automorphims. We show that the exponent of $Aut(X)$ is bounded by $42(g-1)$. We also determine explicitly the infinitely many values of $g$ for which this bound is reached and the corresponding groups. Finally we discuss related questions for subgroups $G$ of $Aut(X)$ that are subject to additional conditions, for example being solvable.

final version, 13 pages, several improvements thanks to the referee

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