Applications of Group Theory to Finite Geometry

群论在有限几何中的应用

• 批准号: DP0450695
• 负责人: Prof Timothy Penttila
• 金额: $ 13.11万
• 依托单位: The University of Western Australia
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2004
• 资助国家: 澳大利亚
• 起止时间: 2004-01-01 至 2006-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0450695
• 关键词: Applications; Group; Theory; Finite; Geometry

Group theory and geometry have influenced one another for over a century. The most important structures in geometry are the symmetric ones and the most important groups act on geometries. Recent developments in finite geometry, although informed by symmetry, have used a minimum of group theory. The project aims to redress this, by applying results from a broad range of finite group theory to the presently hot topics in finite geometry. Our aim is to achieve a paradigm shift, by finding substantively different structures than those presently known. Should it succeed, much activity in geometry would follow, seeking geometric interpretation of these group theoretic results. Our focus is necessitated by the lack of a result characterising the underlying groups of symmetric generalised quadrangles.

群论和几何学相互影响了世纪。几何中最重要的结构是对称结构，最重要的群作用于几何。有限几何学的最新发展，虽然是以对称性为基础的，但只使用了最少的群论。该项目的目的是纠正这一点，通过应用结果从广泛的有限群理论，目前在有限几何的热门话题。我们的目标是通过发现与目前已知的结构实质上不同的结构来实现范式转变。如果它成功了，许多活动在几何将遵循，寻求几何解释这些群论的结果。我们的重点是必要的缺乏一个结果的特点的基本群体的对称广义四边形。