Combinatorial Structures associated with Classical Finite Simple Groups

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 an 8 dimensional
finite orthogonal simple group over the field of q element (q a power of a prime). The aim is
to 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 a
central role in understanding C(G,X).
EPSRC research area: Mathematics/Algebra