Embeddings of Simple Groups in Exceptional Finite Simple Groups
Lead Research Organisation:
University of Manchester
Department Name: Mathematics
Abstract
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 for
E_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 in
determining the possible admissible embeddings.
EPSRC research area: Mathematics/Algebra
E_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 in
determining the possible admissible embeddings.
EPSRC research area: Mathematics/Algebra
Organisations
People |
ORCID iD |
Peter John Rowley (Primary Supervisor) | |
Joseph Parkin (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/T517823/1 | 01/10/2020 | 30/09/2025 | |||
2616638 | Studentship | EP/T517823/1 | 01/10/2021 | 31/03/2025 | Joseph Parkin |