Subgroup Structure of certain Exceptional Finite Simple Groups

本文研究q （q是素数的幂次）的小值有限例外简单群E_8(q)的子群。主要目的之一是发现是否有其他有限简单群H可以作为E_8(q)的子群出现，进而发现它们是否可能是极大的子群。这将涉及研究E_8(q)对它的248维GF(q)-模的作用，从而了解它的共轭类和它的Sylow子群的结构。H的相关属性也会进入到这个分析中。这些组非常大，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该项目。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