Combinatorial Structures associated with Classical Finite Simple Groups

这个项目将研究某些可以利用群G的结构特征来构造的图，目标是确定关于这些图的图论信息，这将反过来揭示群的结构细节。这类图的一个例子是可交换对合图C(G，X)，它的顶点是关于G中的对合的共轭类X，如果它们在G中交换，则C(G，X)中的两个不同的对合是相邻的两个不同的对合。当G是Q元域(Q是素数的幂)上的8维有限正交单群时，研究将首先集中在C(G，X)的圆盘结构上。我们的目的是对所有的Q和正负类型的正交群都这样做。期望G在它的8维正交GF(Q)-模上的作用将对理解C(G，X)起到中心作用。EPSRC研究领域：数学/代数

This project will study certain graphs which can be constructed using structural features of 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