关于4维Laguerre平面的Kleinewillinghöfer型的一个注记

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2022-10-01 DOI:10.1515/advgeom-2022-0020

G. Steinke

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引用次数: 0

摘要

摘要Kleinewillinghöfer在1979年对Laguerre平面的自同构群对中心自同构的线性传递子群进行了分类，得到了许多类型。所有可行的Kleinewillinghöfer二维拉盖尔平面类型在2021年完全确定。本文研究了四维拉盖尔平面的Kleinewillinghöfer类型及其自同构群，并证明了Kleinewillinghöfer所描述的49种类型中，只有12种在四维拉盖尔平面上是可行的。提供了其中四种类型的示例。

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A note on the Kleinewillinghöfer types of 4-dimensional Laguerre planes

Abstract Kleinewillinghöfer classified in 1979 automorphism groups of Laguerre planes with respect to linearly transitive subgroups of central automorphisms and obtained a multitude of types. All feasible Kleinewillinghöfer types of 2-dimensional Laguerre planes were completely determined in 2021. In this paper we investigate the Kleinewillinghöfer types of 4-dimensional Laguerre planes with respect to the automorphism groups of these planes and show that of the 49 types Kleinewillinghöfer described, only twelve are feasible in 4-dimensional Laguerre planes. Examples of four of these type are provided.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.