Combinatorial Structures associated with Classical Finite Simple Groups

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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