Algorithms for fusion systems

Jason Semeraro (Leicester)

Frank Adams 1,

Saturated fusion systems turn up naturally in group theory, representation theory and topology when specialising (suitably interpreted) to a fixed prime \(p\). When \(p=2\) there is a program to mimic the proof of the classification of finite simple groups in order to list all saturated fusion systems which are simple, and there are good conjectures for what this list should include. When \(p\) is odd the structure of (simple) fusion systems is not well-understood, due to the vast number of sporadic structures which arise. A greater understanding would have implications for all of the above areas. We survey recent classification results and present methods which, in favourable cases, will automate the process of listing all saturated fusion systems on a given \(p\)-group. This is ongoing work with Chris Parker.
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