On nilpotent automorphism groups of function fields

Anbar Meidl, Nurdagül and Güneş, Burçin (2022) On nilpotent automorphism groups of function fields. Advances in Geometry, 22 (1). pp. 69-78. ISSN 1615-715X (Print) 1615-7168 (Online)

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Official URL: http://dx.doi.org/10.1515/advgeom-2021-0006

Abstract

We study the automorphisms of a function field of genus g >= 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.

Item Type:	Article
Uncontrolled Keywords:	Function field; Hurwitz Genus Formula; nilpotent group; positive characteristic
Subjects:	Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions:	Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences
Depositing User:	Nurdagül Anbar Meidl
Date Deposited:	11 Feb 2022 14:32
Last Modified:	30 Aug 2022 15:53
URI:	https://research.sabanciuniv.edu/id/eprint/42734

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On nilpotent automorphism groups of function fields. (deposited 25 May 2021 16:45)
- On nilpotent automorphism groups of function fields. (deposited 16 Aug 2021 21:57)
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