用平面函数构造仿射几何(英文)

Constructing Affine Geometries Using Planar Mappings

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摘要短文证明了可以从n阶循环群到它自身的平面函数来构造一类仿射几何.作为推论,证明了n必须是奇素数幂.从而证明了如果存在一个射影平面,它具有一个n^2阶的自同构群,那么n必须是素数幂.这是"素幂猜想"的一个特殊情形. In this note, we find that one can construct affine geometry AG（3, n） using planar mappings from a cyclic group N of order n to itself. As a consequence, n is a prime power. Hence we proved that if there exists a projective plane of order n with a collineation group of order n^2. Then n must be a prime power.

作者曹喜望

机构地区南京航空航天大学理学院数学系信息安全国家重点实验室

出处《数学进展》 CSCD 北大核心 2008年第6期719-723,共5页 Advances in Mathematics（China）

基金 Project supported by NSFC(No.10301033,No.10771100)

关键词平面函数仿射几何射影平面素幂猜想 planar mappings affine geometries projective planes prime power conjecture

分类号 O174.4 [理学—基础数学] O185 [理学—基础数学]

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用平面函数构造仿射几何(英文)

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