Combinatorial Structures associated with Exceptional Finite Simple Groups

该项目将研究可以使用群g的结构特征构建的某些图，目标是确定关于这些图的图理论信息，这些图将反过来揭示群的结构细节。这些图中的一个例子是交换对合图C(G，X)，它的顶点是G中对合上的共轭类X与C（G，X）中相邻的两个不同的对合，如果它们在G中交换，研究将首先集中于当G是例外有限单群G_2(q) （q是素数的幂）时C（G，X）的盘结构。目的是对所有的q都这样做。预计G对其标准GF(q)-模块的作用将在理解C（G，X）中发挥核心作用。EPSRC研究领域：数学/代数

This project will study certain graphs which can be constructed using structural features of a group G. The objective is to determine graph theoretical information about such graphs which will in turn reveal structural details of the group. An example of one of these graphs is the commuting involution graph C(G,X), whose vertices are a conjugacy class X on involutions 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 the exceptional finite simple group G_2(q) (q a power of a prime). The aim is to do this for all q. It is expected that the action of G on its standard GF(q)-module will play a central role inunderstanding C(G,X).EPSRC research area: Mathematics/Algebra