Subgroup Structure of certain Exceptional Finite Simple Groups

本课题将研究有限例外单群E8(Q)的子群中q(q为素数的幂)的小值问题。主要目的之一是发现某些其他有限单群H是否可以作为E_8(Q)的子群出现，以及它们是否可能是极大子群。这涉及到研究E_8(Q)在它的248维GF(Q)-模上的作用，以了解它的共轭类和它的Sylow子群的结构。H的相关性质也将进入这一分析。这些群非常大--例如，E_8(3)大约有10^{123}个元素，预计计算机代数将大量参与这个项目。EPSRC研究领域：数学/代数

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