Combinatorial Structures associated with Classical Finite Simple Groups

与经典有限单群相关的组合结构

• 批准号: 2608958
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2608958
• 关键词: Combinatorial; Structures; associated; Classical; Finite

This project will study certain graphs which can be constructed using structural features of agroup G. The objective is to determine graph theoretical information about such graphswhich will in turn reveal structural details of the group. An example of one of these graphs isthe commuting involution graph C(G,X), whose vertices are a conjugacy class X oninvolutions in G with two distinct involutions adjacent in C(G,X) if they commute in G.Investigations will initially focus on the disc structure of C(G,X) when G is an 8 dimensionalfinite orthogonal simple group over the field of q element (q a power of a prime). The aim isto do this for all q and for plus and minus types of orthogonal groups.It is expected that the action of G on its 8 dimensional orthogonal GF(q)-module will play acentral role in understanding C(G,X).EPSRC research area: Mathematics/Algebra

该项目将研究可以使用g群结构特征构建的某些图，目的是确定有关此类图的图理论信息，这些图将反过来揭示组的结构细节。这些图中的一个例子是交换对合图C(G，X)，它的顶点是一个共轭类X在G上的对合与C（G，X）上相邻的两个不同的对合，如果它们在G上交换，研究将首先集中在C（G，X）的盘结构上，当G是一个8维有限正交单群在q元素（q的一个素数的幂）的域上。我们的目标是对所有q和正、负正交群都这样做。预计G对其8维正交GF(q)-模的作用将在理解C（G，X）中发挥核心作用。EPSRC研究领域：数学/代数