Let $X$ be a compact Riemann surface of genus $g\geq 2$, and let $G$ be asubgroup of $Aut(X)$. We show that if the Sylow $2$-subgroups of $G$ arecyclic, 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 attainedfor infinitely many values of $g$.
展开▼
机译：假设$ X $是$ g \ geq 2 $族的紧黎曼曲面，并且让$ G $是$ Aut（X）$的子组。我们证明，如果$ G $的Sylow $ 2 $-子组是循环的，则$ | G | \ leq 30（g-1）$。如果$ G $的所有Sylow子组都是循环的，则$ | G | \ leq 10（g-1）$除两个例外。更一般而言，如果$ G $是元环的，那么，除了一个例外，$ | G | \ leq 12（g-1）$。对于$ g $的无限多个值，可以达到每个界限。
展开▼
