Embeddings of Simple Groups in 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。主要的焦点之一将是计算E_8(q)和其他各种简单群h的Brauer字符。在这里，了解共轭类，特别是E_8(q)的知识是很重要的。目的是观察在248维GF(q)模forE_8(q)上H的可容许融合和限制可能发生。这将给出H在E_8(q)中可能嵌入的信息，并且在某些情况下将显示这样的H不能嵌入。计算大阶元素的布劳尔字符值有时会有问题。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，特别是确定可能允许的嵌入。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 focuses will be the calculation of Brauer characters for both E_8(q) and also for various other simple groups H. It will be important here to have knowledge of conjugacy classes, particularly of E_8(q). The aim is to see which admissible fusions and restrictions of H on the 248 dimensional GF(q) module forE_8(q) can occur. This will give information on possible embeddings of H in E_8(q) and in some cases will show that such an H cannot be embedded. Calculating the values of Brauer characters of large order elements can some times be problematic. These groups are very large - for example E_8(3) has approximately 10^{123} elements and it is expected that computer algebra will be heavily involved in this project, particularly indetermining the possible admissible embeddings.EPSRC research area: Mathematics/Algebra