Combinatorial Structures associated with Exceptional Finite Simple Groups

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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