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Agroup G的结构特征构建的某些图。目的是确定有关此类GraphSwhich的图形理论信息，又将揭示该组的结构细节。 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).目的是针对所有Q，以及对正交组的加上和减去类型的类型。期望G对其8维正交GF（Q） - 模块的作用在理解C（G，X）.EPSRC研究领域中发挥大的作用。