Embeddings of Simple Groups in 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。其中一个主要的焦点将是E_8(Q)和各种其他简单群H的Brauer特征标的计算。这里重要的是要了解共轭类，特别是E_8(Q)的知识。我们的目的是看看H在248维GF(Q)模FORE_8(Q)上可以发生哪些允许的融合和限制。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表明这样的H不能被嵌入。计算大阶元素的布劳尔特征符值有时可能会有问题。这些群是非常大的-例如，E_8(3)大约有10^{123}个元素，预计计算机代数将在这个项目中大量参与，特别是在确定可能的允许嵌入方面。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