Subgroup Structure of certain Exceptional Finite Simple Groups

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This project will investigate the subgroups of the finite exceptional simple group E_8(q) for small values of q (q a power of a prime). One of the main aims is to discover whether certain other finite simple groups H can occur as subgroups of E_8(q) and, further, whether they could possibly be maximal subgroups. This will involve studying the action of E_8(q) upon its 248 dimensional GF(q)-module so as to understand its conjugacy classes and the structure of its Sylow subgroups. Relevant properties of H will also enter into this analysis. These groups are very large - for example E_8(3) has approximately 10^{123} elements andit is expected that computer algebra will be heavily involved in this project.EPSRC research area: Mathematics/Algebra