"Categories of p-Subgroups"





(University of Copenhagen)




Abstract: Let G be a finite group and p a prime number. The set p-subgroups of G form the object set of at least six different categories: The poset ordered by inclusion, the transporter category, the fusion category, the exterior quotient of the fusion category, the orbit category, the linking category. These categories admit weightings and coweightings defining their Euler characteristics. The (co)weigtings for the various p-subgroup categories seem to carry interesting information: 1. They point to homotopy equivalences between certain subcategories of the p-subgroup categories 2. They relate Frobenius' theorem on the number of solutions in G to g^n=e to Brown's theorem on the Euler characteristic of the poset of p-subgroups 3. They may have something to say about the two big conjectures, Quillen's conjecture on contractibility of p-subgroup posets and  Alperin's Weight Conjecture, in this area. More information can be found here






Date: Wednesday, May 14, 2014

Time: 15.40 16:30

Place: Mathematics Seminar Room, SA-141



Tea and cookies will be served after the seminar.