Embeddings of Simple Groups in Exceptional Finite Simple Groups

简单群在异常有限简单群中的嵌入

• 批准号: 2616638
• 金额: --
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2616638
• 关键词: Embeddings; Simple; Groups; Exceptional; Finite

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

本课题研究有限例外单群E_8（q）的子群，其中q为素数的幂，q为小值。其中一个主要的重点是计算E_8（q）和其他各种单群H的Brauer特征标。在这里了解共轭类，特别是E_8（q）的知识很重要。本文的目的是研究H在248维GF（q）模上对E_8（q）的可容许融合和限制。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不能嵌入。计算高阶元素的Brauer特征值有时会有问题。这些群是非常大的-例如E_8（3）有大约10^{123}个元素，预计计算机代数将大量参与这个项目，特别是在确定可能的容许嵌入。EPSRC研究领域：数学/代数