**"****Categories
of p-Subgroups****"**

By

**(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 http://arxiv.org/abs/math/0610260 http://arxiv.org/abs/1007.1890 http://arxiv.org/abs/1301.0193

**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.