Combinatorial Structures associated with Classical Finite Simple Groups

本计画将研究利用群G的结构特徴所能建构的某些图。我们的目标是确定图论信息，这些graphswhich将反过来揭示组的结构细节。交换对合图C（G，X）就是其中一个例子，它的顶点是G中对合上的共轭类X，如果它们在G中交换，则两个不同的对合在C（G，X）中相邻。当G是q元域上的8维有限正交单群（q是素数的幂）时，研究C（G，X）的圆盘结构。我们的目标是对所有的q和正负类型的正交群都这样做。我们希望G在其8维正交GF（q）-模上的作用将在理解C（G，X）中发挥中心作用。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