Fusion systems on groups with an abelian subgroup of index p

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• David Craven, University of Birmingham
• Thursday 13 November 2014, 16:00-17:00
• Physics West 117.

If you have a question about this talk, please contact David Craven.

The search for exotic fusion systems at odd primes has turned up maybe new systems with a variety of properties. In an attempt to bring order to at least some of the chaos, we classify all exotic fusion systems on p-groups with an abelian subgroup of index p, which encompasses the Ruiz–Viruel examples of fusion systems on the extraspecial group 7₊¹⁺² and the Clelland–Parker examples coming from GL₂(p).

Along the way we meet questions about finite simple groups and their representation theory, and end up classifying indecomposable modules for almost simple groups with the property that the Sylow p-subgroup has order p, and the module M has only one non-trivial summand when restricted to the Sylow p-subgroup. The theory then essentially provides a dictionary between these and new fusion systems, leading to a wealth of new examples, including another infinite family and several sporadic examples.

This talk is part of the Algebra seminar series.

This talk is included in these lists:

• Algebra seminar
• Physics West 117
• School of Mathematics events

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