University of Birmingham > Talks@bham > Algebra Seminar > Fusion systems on groups with an abelian subgroup of index p

Fusion systems on groups with an abelian subgroup of index p

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  • UserDavid Craven, University of Birmingham
  • ClockThursday 13 November 2014, 16:00-17:00
  • HousePhysics 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.

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