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Identifying finite simple groups from their fusion systems

Project Description

Groups are fundamental algebraic structures closely related to describing and understanding symmetry. Every group is built up of building blocks which cannot be split up any further. These building blocks are called simple groups. The combined effort of many mathematicians culminated in the classification of all finite simple groups, which is often regarded as one of the major mathematical achievements of the 20th century. Its importance lies not only in the fundamental result, but also in the methodology and the conceptual framework developed for its proof. Most intriguingly, it turned out that the structure of a finite group is closely connected to the structure of the p-local subgroups, i.e. the normalizers of non-trivial p-subgroups, for a suitably chosen prime p. Of particular importance is the prime 2.

Aschbacher suggested a modern approach to the classification of finite simple groups via so-called saturated fusion systems. To implement this approach one will need to identify a finite group from some information which is slightly weaker than the knowledge of the p-local subgroups. More precisely, one will need to identify a finite group G from the knowledge of NG(P)/CG(P) for all non-trivial p-subgroups P of G and the knowledge of a Sylow p-subgroup of G. Prospective students could show that the members of a family of finite simple groups of Lie type are determined by this data.

Candidates should have (or expect to achieve) a UK honours degree at 2.1 or above (or equivalent) in Mathematics.

It is essential that the successful applicant has a background in Group Theory along with knowledge of Finite group theory.


• Apply for Degree of Doctor of Philosophy in Mathematics
• State name of the lead supervisor as the Name of Proposed Supervisor
• State ‘Self-funded’ as Intended Source of Funding
• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)
• Detailed CV
• Details of 2 academic referees

Informal inquiries can be made to Dr Ellen Henke () with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ()

Funding Notes

This project is advertised in relation to the research areas of the discipline of Mathematics. The successful applicant will be expected to provide the funding for Tuition fees, living expenses and maintenance. Details of the cost of study can be found by visiting View Website. THERE IS NO FUNDING ATTACHED TO THESE PROJECTS.

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