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arXiv · 1912.08146

On nilpotent automorphism groups of function fields

Nurdagül Anbar·Burçin Güneş
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Abstract

We study the automorphisms of a function field of genus $g\geq 2$ over an algebraically closed field of characteristic $p>0$. More precisely, we show that the order of a nilpotent subgroup $G$ of its automorphism group is bounded by $16 (g-1)$ when G is not a $p$-group. We show that if $|G|=16(g-1) $, then $g-1$ is a power of $2$. Furthermore, we provide an infinite family of function fields attaining the bound.

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Nurdagül Anbar, Burçin Güneş. 2019-12-17. On nilpotent automorphism groups of function fields. https://arxiv.org/abs/1912.08146

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